Deck 5: Normal, binomial, poisson, and Exponential Distributions

Question 1

Given that Z is a standard normal random variable,P(-1.0 Z 1.5)is

A)0.7745
B)0.8413
C)0.0919
D)0.9332

Answer 1

A

Question 2

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 the above

Answer 2

B

Question 3

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

Answer 3

D

Question 4

Which of the following equations shows the process of standardizing?

A)
B)
C)
D)

Question 5

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

Question 6

A Poisson distribution is:

A)relevant when we sample from a population with only two types of members.
B)relevant when we perform a series of independent,identical experiments with only two possible outcomes.
C)usually relevant when we are interested in the number of events that occur over a given interval of time
D)the cornerstone of statistical theory
E)All of the above

Question 7

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

Question 8

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

Question 9

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 the above

Question 10

The normal distribution is:

A)a discrete distribution with two parameters
B)a binomial distribution with only one parameter
C)a density function of a discrete random variable
D)a continuous distribution with two parameters

Question 11

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

Question 12

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

Question 13

The mean of a probability distribution is a:

A)measure of variability of the distribution
B)measure of central location
C)measure of relative likelihood
D)measure of skewness of the distribution

Question 14

Which probability distribution applies to the number of events occurring within a specified period of time or space

A)Binomial distribution
B)Poisson distribution
C)Any discrete probability distribution
D)Any continuous probability distribution

Question 15

The Poisson random variable is a:

A)discrete random variable with infinitely many possible values
B)discrete random variable with finite number of possible values
C)continuous random variable with infinitely many possible values
D)continuous random variable with finite number of possible values

Question 16

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

Question 17

The variance of a binomial distribution for which n = 100 and p = 0.20 is:

A)100
B)80
C)20
D)16

Question 18

Tossing a coin is an example of a (n)

A)binomial distribution
B)normal distribution
C)exponential distribution
D)Poisson distribution

Question 19

The standard deviation of a probability distribution is a:

A)measure of variability of the distribution
B)measure of central location
C)measure of relative likelihood
D)measure of skewness of the distribution

Question 20

If we plot a continuous probability distribution f(x),the total probability under the curve is

A)-1
B)0
C)1
D)100

Question 21

The number of loan defaults per month at a bank is Poisson distributed.

Question 22

Using the standard normal distribution,the Z-score representing the 5th percentile is 1.645.

Question 23

The total area under the normal distribution curve is equal to one.

Question 24

Given that Z is a standard normal variable,the value z for which P(Z z)= 0.2580 is

A)0.70
B)0.758
C)-0.65
D)0.242

Question 25

If the random variable X is exponentially distributed with parameter = 3,then P(X 2),up to 4 decimal places ,is

A)0.3333
B)0.5000
C)0.6667
D)0.0025

Question 26

If the random variable X is exponentially distributed with parameter = 1.5,then P(2 X 4),up to 4 decimal places,is

A)0.6667
B)0.0473
C)0.5000
D)0.2500

Question 27

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.

Question 28

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.

Question 29

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.

Question 30

If the mean of an exponential distribution is 2,then the value of the parameter is

A)4
B)2
C)1
D)0.5

Question 31

Much of the study of probabilistic inventory models,queuing models,and reliability models relies heavily on the Poisson and Exponential distributions.

Question 32

Poisson distribution is appropriate to determine the probability of a given number of defective items in a shipment.

Question 33

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

A)0.5328
B)0.3413
C)0.1915
D)0.1498

Question 34

The Poisson probability distribution is one of the most commonly used continuous probability distributions.

Question 35

The binomial distribution is a discrete distribution that deals with a sequence of identical trials,each of which has only two possible outcomes.

Question 36

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

Question 37

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.

Question 38

The Poisson and Exponential distributions are commonly used in which of the following applications

A)Inventory models
B)Financial models
C)Failure analysis models
D)All of these options

Question 39

Which of the following distributions is appropriate to measure the length of time between arrivals at a grocery checkout counter?

A)Uniform
B)Normal
C)Exponential
D)Poisson

Question 40

The binomial distribution is a continuous distribution that is not far behind the normal distribution in order of importance.

Question 41

What is the probability that a randomly selected customer will spend less than $15?

Question 42

An exponential distribution with parameter = 0.2 has mean and standard deviation both equal to 5.

Question 43

The binomial random variable represents the number of successes that occur in a specific period of time.

Question 44

Using the standard normal curve,the Z- score representing the 10th percentile is 1.28.

Question 45

The binomial distribution deals with consecutive trials,each of which has two possible outcomes.

Question 46

The Poisson distribution is applied to events for which the probability of occurrence over a given span of time,space,or distance is very small.

Question 47

Using the standard normal distribution,the Z- score representing the 99th percentile is 2.326.

Question 48

What is the probability that a randomly selected customer will spend $20 or more?

Question 49

The Poisson distribution is characterized by a single parameter ,which must be positive.

Question 50

What is the probability that a randomly selected customer will spend between $20 and $35?

Question 51

What two dollar amounts,equidistant from the mean of $30,such that 98% of all customer purchases are between these values?

Question 52

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.

Question 53

The mean and standard deviation of a normally distributed random variable which has been "standardized" are zero and one,respectively.

Question 54

What is the probability that a randomly selected customer will spend $30 or more?

Question 55

The variance of a binomial distribution for which n = 50 and p = 0.20 is 8.0.

Question 56

What two dollar amounts,equidistant from the mean of $30,such that 90% of all customer purchases are between these values?

Question 57

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.

Question 58

There is a 5% chance that GM will sell more than what number of cars during the next year?

Question 59

Using the standard normal curve,the Z- score representing the 75th percentile is 0.674.

Question 60

The Poisson random variable is a discrete random variable with infinitely many possible values.

Question 61

What number of cars,equidistant from the mean,such that 90% of car sales are between these values?

Question 62

What is the probability that GM will sell between 2.0 and 2.3 million cars during the next year?

Question 63

What is the probability that this company will sell between 2.0 and 2.15 million cars next year?

Question 64

What is the probability that none of the 20 new microwaves sold will require a warranty repair in the first 90 days?

Question 65

What is the probability that less than two of the 20 new microwaves sold will require a warranty repair in the first 90 days?

Question 66

How many chicken sandwiches must the restaurant stock to be 99% sure of not running out on a given day?

Question 67

Calculate the mean,variance,and standard deviation for the entire year (assume 52 weeks in the year).

Question 68

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.

Question 69

What type of probability distribution will most likely be used to analyze warranty repair needs on new microwaves in this situation?

Question 70

What number of cars,equidistant from the mean,such that 98% of car sales are between these values?

Question 71

Why is the independence assumption in Question 74 probably not realistic? Using a more realistic assumption,do you think the probability in Question 74 would increase or decrease?

Question 72

What is the probability that exactly two of the 20 new microwaves sold will require a warranty repair in the first 90 days?

Question 73

Only 5% of the students taking the test scored higher than what value?

Question 74

What is the probability of getting a score higher than 85 on this exam?

Question 75

What is the probability that exactly half the male adults will be less than 62 inches tall?

Question 76

What percentage of students scored between 81 and 89 on this exam?

Question 77

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.

Question 78

What is the probability that this company will sell more than 2 million cars next year?

Question 79

How many hamburgers must the restaurant stock to be 99% sure of not running out on a given day?

Question 80

There is a 1% chance that this company will sell more than what number of cars during the next year?