Deck 5: Normal, Binomial, Poisson, and Exponential Distributions

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سؤال
The standard deviation <strong>The standard deviation   of a probability distribution is a measure of:</strong> A) variability of the distribution B) central location C) relative likelihood D) skewness of the distribution <div style=padding-top: 35px> of a probability distribution is a measure of:

A) variability of the distribution
B) central location
C) relative likelihood
D) skewness of the distribution
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سؤال
If the value of the standard normal random variable Z is positive, then the original score is where in relationship to the mean?

A) equal to the mean
B) to the left of the mean
C) to the right of the mean
D) none of these choices
سؤال
The normal distribution is a:

A) discrete distribution with two parameters
B) binomial distribution with only one parameter
C) density function of a discrete random variable
D) continuous distribution with two parameters
سؤال
Given that Z is a standard normal random variable, P(-1.0 <strong>Given that Z is a standard normal random variable, P(-1.0   Z   1.5) is:</strong> A) 0.7745 B) 0.8413 C) 0.0919 D) 0.9332 <div style=padding-top: 35px> Z <strong>Given that Z is a standard normal random variable, P(-1.0   Z   1.5) is:</strong> A) 0.7745 B) 0.8413 C) 0.0919 D) 0.9332 <div style=padding-top: 35px> 1.5) is:

A) 0.7745
B) 0.8413
C) 0.0919
D) 0.9332
سؤال
A random variable X is standardized when each value of X has the mean of X subtracted from it, and the difference is divided by the standard deviation of X.
سؤال
One reason for standardizing random variables is to measure variables with:

A) different means and standard deviations on a non-standard scale
B) different means and standard deviations on a single scale
C) dissimilar means and standard deviations in like terms
D) similar means and standard deviations on two scales
سؤال
The standard normal distribution has a mean and a standard deviation respectively equal to:

A) 0 and 0
B) 1 and 1
C) 1 and 0
D) 0 and 1
سؤال
Using the standard normal distribution, the Z-score representing the 5th percentile is 1.645.
سؤال
The mean <strong>The mean   of a probability distribution is a measure of:</strong> A) variability of the distribution B) central location C) relative likelihood D) skewness of the distribution <div style=padding-top: 35px> of a probability distribution is a measure of:

A) variability of the distribution
B) central location
C) relative likelihood
D) skewness of the distribution
سؤال
If the random variable X is normally distributed with mean If the random variable X is normally distributed with mean   and standard deviation   , then the random variable Z defined by   is also normally distributed with mean 0 and standard deviation 1.<div style=padding-top: 35px> and standard deviation If the random variable X is normally distributed with mean   and standard deviation   , then the random variable Z defined by   is also normally distributed with mean 0 and standard deviation 1.<div style=padding-top: 35px> , then the random variable Z defined by If the random variable X is normally distributed with mean   and standard deviation   , then the random variable Z defined by   is also normally distributed with mean 0 and standard deviation 1.<div style=padding-top: 35px> is also normally distributed with mean 0 and standard deviation 1.
سؤال
The total area under the normal distribution curve is equal to one.
سؤال
Which equation shows the process of standardizing?

A) <strong>Which equation shows the process of standardizing?</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Which equation shows the process of standardizing?</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Which equation shows the process of standardizing?</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Which equation shows the process of standardizing?</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Which of the following might not be appropriately modeled with a normal distribution?

A) the daily low temperature in Anchorage, Alaska
B) the returns on a stock
C) the daily change in inventory at a computer manufacturer
D) the salaries of employees at a large company
سؤال
Given that the random variable X is normally distributed with a mean of 80 and a standard deviation of 10, P(85 <strong>Given that the random variable X is normally distributed with a mean of 80 and a standard deviation of 10, P(85   X   90) is:</strong> A) 0.5328 B) 0.3413 C) 0.1915 D) 0.1498 <div style=padding-top: 35px> X <strong>Given that the random variable X is normally distributed with a mean of 80 and a standard deviation of 10, P(85   X   90) is:</strong> A) 0.5328 B) 0.3413 C) 0.1915 D) 0.1498 <div style=padding-top: 35px> 90) is:

A) 0.5328
B) 0.3413
C) 0.1915
D) 0.1498
سؤال
If X is a normal random variable with a standard deviation of 10, then 3X has a standard deviation equal to:

A) 10
B) 13
C) 30
D) 90
سؤال
Given that Z is a standard normal variable, the value z for which P(Z <strong>Given that Z is a standard normal variable, the value z for which P(Z   z) = 0.2580 is:</strong> A) 0.70 B) 0.758 C) -0.65 D) 0.242 <div style=padding-top: 35px> z) = 0.2580 is:

A) 0.70
B) 0.758
C) -0.65
D) 0.242
سؤال
If we plot a continuous probability distribution f(x), the total probability under the curve is:

A) -1
B) 0
C) 1
D) 100
سؤال
What two dollar amounts, equidistant from the mean of $30, such that 98% of all customer purchases are between these values?
سؤال
The higher the value of the density function f(x), _____.

A) the less likely the value x
B) the more likely the value x
C) the less likely the distribution is normal
D) none of these choices is likely
سؤال
A continuous probability distribution is characterized by:

A) a list of possible values
B) counts
C) an array of individual values
D) a continuum of possible values
سؤال
There is a 1% chance that this company will sell more than what number of cars during the next year?
سؤال
What number of cars, equidistant from the mean, such that 98% of car sales are between these values?
سؤال
The mean and standard deviation of a normally distributed random variable that has been "standardized" are zero and one, respectively.
سؤال
Calculate the mean, variance, and standard deviation for the entire year (assume 52 weeks in the year).
سؤال
If the restaurant stocks 600 hamburgers and 150 chicken sandwiches for a given day, what is the probability that it will run out of hamburgers or chicken sandwiches (or both) that day? Assume that the demands for hamburgers and chicken sandwiches are probabilistically independent.
سؤال
What two dollar amounts, equidistant from the mean of $30, such that 90% of all customer purchases are between these values?
سؤال
What is the probability that this company will sell between 2.0 and 2.15 million cars next year?
سؤال
Using the standard normal distribution, the Z- score representing the 99th percentile is 2.326.
سؤال
How many chicken sandwiches must the restaurant stock to be 99% sure of not running out on a given day?
سؤال
What number of cars, equidistant from the mean, such that 90% of car sales are between these values?
سؤال
Using the standard normal curve, the Z- score representing the 75th percentile is 0.674.
سؤال
What is the probability that a randomly selected customer will spend less than $15?
سؤال
What is the probability that a randomly selected customer will spend $20 or more?
سؤال
What is the probability that a randomly selected customer will spend $30 or more?
سؤال
There is a 5% chance that GM will sell more than what number of cars during the next year?
سؤال
Using the standard normal curve, the Z- score representing the 10th percentile is 1.28.
سؤال
What is the probability that a randomly selected customer will spend between $20 and $35?
سؤال
What is the probability that this company will sell more than 2 million cars next year?
سؤال
A random variable X is normally distributed with a mean of 175 and a standard deviation of 50. Given that X = 150, its corresponding Z- score is -0.50.
سؤال
What is the probability that GM will sell between 2.0 and 2.3 million cars during the next year?
سؤال
​A restaurant stocks 600 hamburgers and 150 chicken sandwiches for a given day. Assume that the demands for hamburgers and chicken sandwiches are probabilistically independent. Why is the independence assumption in this scenario probably not realistic? Using a more realistic assumption, do you think the probability would increase or decrease?
سؤال
What is the probability of getting a score higher than 85 on this exam?
سؤال
Only 5% of the students taking the test scored higher than what value?
سؤال
What percentage of students scored between 81 and 89 on this exam?
سؤال
According to the empirical rule, how many observations lie within +/- 2 standard deviation from the mean?​

A) ​50%
B) ​68%
C) ​95%
D) ​almost all
سؤال
The variance of a binomial distribution is given by the formula The variance of a binomial distribution is given by the formula   , where n is the number of trials, and p is the probability of success in any trial.<div style=padding-top: 35px> , where n is the number of trials, and p is the probability of success in any trial.
سؤال
The results of tossing a coin can be portrayed in a(n):

A) binomial distribution
B) normal distribution
C) exponential distribution
D) Poisson distribution
سؤال
A binomial distribution with n number of trials, and probability of success p can be approximated well by a normal distribution with mean np and variance A binomial distribution with n number of trials, and probability of success p can be approximated well by a normal distribution with mean np and variance   if np > 5 and n(1-p) > 5.<div style=padding-top: 35px> if np > 5 and n(1-p) > 5.
سؤال
For a given probability of success p that is not too close to 0 or 1, the binomial distribution tends to take on more of a symmetric bell shape as the number of trials n increases.
سؤال
The binomial distribution is a discrete distribution that deals with a sequence of identical trials, each of which has only two possible outcomes.
سؤال
The binomial distribution is a continuous distribution that is not far behind the normal distribution in order of importance.
سؤال
According to the empirical rule, how many observations lie within +/- 3 standard deviation from the mean?​

A) ​50%
B) ​68%
C) ​95%
D) ​almost all
سؤال
The variance of a binomial distribution for which n = 100 and p = 0.20 is:

A) 100
B) 80
C) 20
D) 16
سؤال
The binomial probability distribution is used with:

A) a discrete random variable
B) a continuous random variable
C) either a discrete or a continuous random variable, depending on the variance
D) either a discrete or a continuous random variable, depending on the sample size
سؤال
The binomial random variable represents the number of successes that occur in a specific period of time.
سؤال
According to the empirical rule, how many observations lie within +/- 1 standard deviation from the mean?​

A) ​50%
B) ​68%
C) ​95%
D) ​almost all
سؤال
The density function specifies the probability distribution of a continuous random variable.​
سؤال
Sampling done without replacement means that:

A) only certain members of the population can be sampled
B) each member of the population can be sampled repeatedly
C) each member of the population can be sampled only once
D) each member of the population can be sampled twice
سؤال
We assume that the outcomes of successive trials in a binomial experiment are:

A) probabilistically independent
B) probabilistically dependent
C) identical from trial to trial
D) random number between 0 and 1
سؤال
How many hamburgers must the restaurant stock to be 99% sure of not running out on a given day?
سؤال
Find the probability distribution of X.
سؤال
Let Y be the number of the 12 male adults who are less than 62 inches tall. Determine the mean and standard deviation of Y.
سؤال
What is the probability that exactly two of the 20 new microwaves sold will require a warranty repair in the first 90 days?
سؤال
What is the probability that only one of the 20 new microwaves sold will require a warranty repair in the first 90 days?
سؤال
Find P(X < 3).
سؤال
What is the probability that at most two of the 20 new microwaves sold will require a warranty repair in the first 90 days?
سؤال
What is the probability that exactly half the male adults will be less than 62 inches tall?
سؤال
What is the probability that between two and four (inclusive) of the 20 new microwaves sold will require a warranty repair in the first 90 days?
سؤال
What is the probability that less than two of the 20 new microwaves sold will require a warranty repair in the first 90 days?
سؤال
Find P(2 Find P(2   X   4).<div style=padding-top: 35px> X Find P(2   X   4).<div style=padding-top: 35px> 4).
سؤال
What is the probability that none of the 20 new microwaves sold will require a warranty repair in the first 90 days?
سؤال
What is the probability that more than one of the 20 new microwaves sold will require a warranty repair in the first 90 days?
سؤال
The binomial distribution deals with consecutive trials, each of which has two possible outcomes.
سؤال
What is the probability that at least one of the 20 new microwaves sold will require a warranty repair in the first 90 days?
سؤال
What is the expected number of the new microwaves sold that will require a warranty repair in the first 90 days?
سؤال
The variance of a binomial distribution for which n = 50 and p = 0.20 is 8.0.
سؤال
Find the mean and the variance of X.
سؤال
What is the standard deviation of the number of the new microwaves sold that will require a warranty repair in the first 90 days?
سؤال
What type of probability distribution will most likely be used to analyze warranty repair needs on new microwaves in this situation?
سؤال
What is the probability that between three and six (exclusive) of the 20 new microwaves sold will require a warranty repair in the first 90 days?
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Deck 5: Normal, Binomial, Poisson, and Exponential Distributions
1
The standard deviation <strong>The standard deviation   of a probability distribution is a measure of:</strong> A) variability of the distribution B) central location C) relative likelihood D) skewness of the distribution of a probability distribution is a measure of:

A) variability of the distribution
B) central location
C) relative likelihood
D) skewness of the distribution
variability of the distribution
2
If the value of the standard normal random variable Z is positive, then the original score is where in relationship to the mean?

A) equal to the mean
B) to the left of the mean
C) to the right of the mean
D) none of these choices
to the right of the mean
3
The normal distribution is a:

A) discrete distribution with two parameters
B) binomial distribution with only one parameter
C) density function of a discrete random variable
D) continuous distribution with two parameters
continuous distribution with two parameters
4
Given that Z is a standard normal random variable, P(-1.0 <strong>Given that Z is a standard normal random variable, P(-1.0   Z   1.5) is:</strong> A) 0.7745 B) 0.8413 C) 0.0919 D) 0.9332 Z <strong>Given that Z is a standard normal random variable, P(-1.0   Z   1.5) is:</strong> A) 0.7745 B) 0.8413 C) 0.0919 D) 0.9332 1.5) is:

A) 0.7745
B) 0.8413
C) 0.0919
D) 0.9332
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5
A random variable X is standardized when each value of X has the mean of X subtracted from it, and the difference is divided by the standard deviation of X.
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6
One reason for standardizing random variables is to measure variables with:

A) different means and standard deviations on a non-standard scale
B) different means and standard deviations on a single scale
C) dissimilar means and standard deviations in like terms
D) similar means and standard deviations on two scales
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7
The standard normal distribution has a mean and a standard deviation respectively equal to:

A) 0 and 0
B) 1 and 1
C) 1 and 0
D) 0 and 1
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8
Using the standard normal distribution, the Z-score representing the 5th percentile is 1.645.
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9
The mean <strong>The mean   of a probability distribution is a measure of:</strong> A) variability of the distribution B) central location C) relative likelihood D) skewness of the distribution of a probability distribution is a measure of:

A) variability of the distribution
B) central location
C) relative likelihood
D) skewness of the distribution
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10
If the random variable X is normally distributed with mean If the random variable X is normally distributed with mean   and standard deviation   , then the random variable Z defined by   is also normally distributed with mean 0 and standard deviation 1. and standard deviation If the random variable X is normally distributed with mean   and standard deviation   , then the random variable Z defined by   is also normally distributed with mean 0 and standard deviation 1. , then the random variable Z defined by If the random variable X is normally distributed with mean   and standard deviation   , then the random variable Z defined by   is also normally distributed with mean 0 and standard deviation 1. is also normally distributed with mean 0 and standard deviation 1.
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11
The total area under the normal distribution curve is equal to one.
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12
Which equation shows the process of standardizing?

A) <strong>Which equation shows the process of standardizing?</strong> A)   B)   C)   D)
B) <strong>Which equation shows the process of standardizing?</strong> A)   B)   C)   D)
C) <strong>Which equation shows the process of standardizing?</strong> A)   B)   C)   D)
D) <strong>Which equation shows the process of standardizing?</strong> A)   B)   C)   D)
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13
Which of the following might not be appropriately modeled with a normal distribution?

A) the daily low temperature in Anchorage, Alaska
B) the returns on a stock
C) the daily change in inventory at a computer manufacturer
D) the salaries of employees at a large company
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14
Given that the random variable X is normally distributed with a mean of 80 and a standard deviation of 10, P(85 <strong>Given that the random variable X is normally distributed with a mean of 80 and a standard deviation of 10, P(85   X   90) is:</strong> A) 0.5328 B) 0.3413 C) 0.1915 D) 0.1498 X <strong>Given that the random variable X is normally distributed with a mean of 80 and a standard deviation of 10, P(85   X   90) is:</strong> A) 0.5328 B) 0.3413 C) 0.1915 D) 0.1498 90) is:

A) 0.5328
B) 0.3413
C) 0.1915
D) 0.1498
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15
If X is a normal random variable with a standard deviation of 10, then 3X has a standard deviation equal to:

A) 10
B) 13
C) 30
D) 90
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16
Given that Z is a standard normal variable, the value z for which P(Z <strong>Given that Z is a standard normal variable, the value z for which P(Z   z) = 0.2580 is:</strong> A) 0.70 B) 0.758 C) -0.65 D) 0.242 z) = 0.2580 is:

A) 0.70
B) 0.758
C) -0.65
D) 0.242
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17
If we plot a continuous probability distribution f(x), the total probability under the curve is:

A) -1
B) 0
C) 1
D) 100
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18
What two dollar amounts, equidistant from the mean of $30, such that 98% of all customer purchases are between these values?
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19
The higher the value of the density function f(x), _____.

A) the less likely the value x
B) the more likely the value x
C) the less likely the distribution is normal
D) none of these choices is likely
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20
A continuous probability distribution is characterized by:

A) a list of possible values
B) counts
C) an array of individual values
D) a continuum of possible values
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21
There is a 1% chance that this company will sell more than what number of cars during the next year?
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22
What number of cars, equidistant from the mean, such that 98% of car sales are between these values?
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23
The mean and standard deviation of a normally distributed random variable that has been "standardized" are zero and one, respectively.
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24
Calculate the mean, variance, and standard deviation for the entire year (assume 52 weeks in the year).
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25
If the restaurant stocks 600 hamburgers and 150 chicken sandwiches for a given day, what is the probability that it will run out of hamburgers or chicken sandwiches (or both) that day? Assume that the demands for hamburgers and chicken sandwiches are probabilistically independent.
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26
What two dollar amounts, equidistant from the mean of $30, such that 90% of all customer purchases are between these values?
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27
What is the probability that this company will sell between 2.0 and 2.15 million cars next year?
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28
Using the standard normal distribution, the Z- score representing the 99th percentile is 2.326.
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29
How many chicken sandwiches must the restaurant stock to be 99% sure of not running out on a given day?
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30
What number of cars, equidistant from the mean, such that 90% of car sales are between these values?
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31
Using the standard normal curve, the Z- score representing the 75th percentile is 0.674.
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32
What is the probability that a randomly selected customer will spend less than $15?
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33
What is the probability that a randomly selected customer will spend $20 or more?
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34
What is the probability that a randomly selected customer will spend $30 or more?
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35
There is a 5% chance that GM will sell more than what number of cars during the next year?
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36
Using the standard normal curve, the Z- score representing the 10th percentile is 1.28.
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37
What is the probability that a randomly selected customer will spend between $20 and $35?
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38
What is the probability that this company will sell more than 2 million cars next year?
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39
A random variable X is normally distributed with a mean of 175 and a standard deviation of 50. Given that X = 150, its corresponding Z- score is -0.50.
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40
What is the probability that GM will sell between 2.0 and 2.3 million cars during the next year?
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41
​A restaurant stocks 600 hamburgers and 150 chicken sandwiches for a given day. Assume that the demands for hamburgers and chicken sandwiches are probabilistically independent. Why is the independence assumption in this scenario probably not realistic? Using a more realistic assumption, do you think the probability would increase or decrease?
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42
What is the probability of getting a score higher than 85 on this exam?
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43
Only 5% of the students taking the test scored higher than what value?
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44
What percentage of students scored between 81 and 89 on this exam?
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45
According to the empirical rule, how many observations lie within +/- 2 standard deviation from the mean?​

A) ​50%
B) ​68%
C) ​95%
D) ​almost all
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46
The variance of a binomial distribution is given by the formula The variance of a binomial distribution is given by the formula   , where n is the number of trials, and p is the probability of success in any trial. , where n is the number of trials, and p is the probability of success in any trial.
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47
The results of tossing a coin can be portrayed in a(n):

A) binomial distribution
B) normal distribution
C) exponential distribution
D) Poisson distribution
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48
A binomial distribution with n number of trials, and probability of success p can be approximated well by a normal distribution with mean np and variance A binomial distribution with n number of trials, and probability of success p can be approximated well by a normal distribution with mean np and variance   if np > 5 and n(1-p) > 5. if np > 5 and n(1-p) > 5.
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49
For a given probability of success p that is not too close to 0 or 1, the binomial distribution tends to take on more of a symmetric bell shape as the number of trials n increases.
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50
The binomial distribution is a discrete distribution that deals with a sequence of identical trials, each of which has only two possible outcomes.
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51
The binomial distribution is a continuous distribution that is not far behind the normal distribution in order of importance.
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52
According to the empirical rule, how many observations lie within +/- 3 standard deviation from the mean?​

A) ​50%
B) ​68%
C) ​95%
D) ​almost all
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53
The variance of a binomial distribution for which n = 100 and p = 0.20 is:

A) 100
B) 80
C) 20
D) 16
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54
The binomial probability distribution is used with:

A) a discrete random variable
B) a continuous random variable
C) either a discrete or a continuous random variable, depending on the variance
D) either a discrete or a continuous random variable, depending on the sample size
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55
The binomial random variable represents the number of successes that occur in a specific period of time.
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56
According to the empirical rule, how many observations lie within +/- 1 standard deviation from the mean?​

A) ​50%
B) ​68%
C) ​95%
D) ​almost all
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57
The density function specifies the probability distribution of a continuous random variable.​
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58
Sampling done without replacement means that:

A) only certain members of the population can be sampled
B) each member of the population can be sampled repeatedly
C) each member of the population can be sampled only once
D) each member of the population can be sampled twice
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59
We assume that the outcomes of successive trials in a binomial experiment are:

A) probabilistically independent
B) probabilistically dependent
C) identical from trial to trial
D) random number between 0 and 1
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60
How many hamburgers must the restaurant stock to be 99% sure of not running out on a given day?
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61
Find the probability distribution of X.
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62
Let Y be the number of the 12 male adults who are less than 62 inches tall. Determine the mean and standard deviation of Y.
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63
What is the probability that exactly two of the 20 new microwaves sold will require a warranty repair in the first 90 days?
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64
What is the probability that only one of the 20 new microwaves sold will require a warranty repair in the first 90 days?
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65
Find P(X < 3).
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66
What is the probability that at most two of the 20 new microwaves sold will require a warranty repair in the first 90 days?
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67
What is the probability that exactly half the male adults will be less than 62 inches tall?
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68
What is the probability that between two and four (inclusive) of the 20 new microwaves sold will require a warranty repair in the first 90 days?
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69
What is the probability that less than two of the 20 new microwaves sold will require a warranty repair in the first 90 days?
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70
Find P(2 Find P(2   X   4). X Find P(2   X   4). 4).
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71
What is the probability that none of the 20 new microwaves sold will require a warranty repair in the first 90 days?
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72
What is the probability that more than one of the 20 new microwaves sold will require a warranty repair in the first 90 days?
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73
The binomial distribution deals with consecutive trials, each of which has two possible outcomes.
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74
What is the probability that at least one of the 20 new microwaves sold will require a warranty repair in the first 90 days?
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75
What is the expected number of the new microwaves sold that will require a warranty repair in the first 90 days?
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76
The variance of a binomial distribution for which n = 50 and p = 0.20 is 8.0.
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77
Find the mean and the variance of X.
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78
What is the standard deviation of the number of the new microwaves sold that will require a warranty repair in the first 90 days?
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79
What type of probability distribution will most likely be used to analyze warranty repair needs on new microwaves in this situation?
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80
What is the probability that between three and six (exclusive) of the 20 new microwaves sold will require a warranty repair in the first 90 days?
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