Question 1

The probability distribution for the daily demand of laptops at a local store is shown below. In this distribution, the random variable x is the daily demand of laptops:  The mean (average) value of x is ___.
A) 1.4
B) 1.75
C) 2.10
D) 2.55
E) 3.02

Accepted Answer

The answer of The probability distribution for the daily demand...

Question 2

At A-Life Corporation, managers begin at $35/hour until they reach $50/hour (salaries are always to the nearest dollar). If the variable x = hourly wage has a discrete uniform distribution, what is the mean wage for the managers?
A) $28.33
B) $35.00
C) $37.50
D) $42.50
E) $50.00

Accepted Answer

The mean of a discrete uniform distribution is calculated as the average of the minimum and maximum values. Here, the minimum wage is $35 and the maximum is $50, so the mean is ($35 + $50) / 2 = $42.50.

Question 3

The probability distribution for the daily demand of laptops at a local store is shown below. In this distribution, the random variable x is the daily demand of laptops:  The standard deviation of x is ___.
A) 1.02
B) 0.89
C) 1.40
D) .506
E) .588

Accepted Answer

The answer of The probability distribution for the daily demand...

Question 4

At A-Life Corporation, managers begin at $35/hour until they reach $50/hour (salaries are always to the nearest dollar). If the variable x = hourly wage has a discrete uniform distribution, what is the standard deviation of x?
A) $7.50
B) $37.50
C) $42.50
D) $50.00
E) $56.25

Accepted Answer

The standard deviation of a discrete uniform distribution is calculated using the formula: SD = sqrt((b-a+1)^2 - 1)/12, where a is the minimum value and b is the maximum value. Here, a = 35 and b = 50, so SD = sqrt((50-35+1)^2 - 1)/12 = sqrt(16^2 - 1)/12 = sqrt(255)/12 ≈ 7.50.

Question 5

The distribution of the number grade one students per household in a rural community is shown below. In this distribution, the random variable x is the number grade one students per household:  The mean (average) value of x is ___.
A) 1.0
B) 1.5
C) 2.0
D) 2.5
E) 3.0

Accepted Answer

The answer of The distribution of the number grade one...

Question 6

Twenty-five individuals are randomly selected out of 100 shoppers leaving a local bedding store. Each shopper was asked if they made a purchase during their visit. Each of the shoppers has the same probability of answering 'yes' to having made a purchase. The probability that exactly four of the twenty-five shoppers made a purchase could best be found by ___.
A) using the normal distribution
B) using the binomial distribution
C) using the Poisson distribution
D) using the exponential distribution
E) using the uniform distribution

Accepted Answer

The situation described fits the criteria for a binomial distribution. We have a fixed number of trials (25 shoppers), each trial has only two possible outcomes (purchase or no purchase), the trials are independent, and the probability of success (a purchase) is the same for each trial. Therefore, we can use the binomial distribution to find the probability of exactly four of the twenty-five shoppers making a purchase.

Question 7

The distribution of the number grade one students per household in a rural community is shown below. In this distribution, the random variable x is the number grade one students per household:  The standard deviation of x is ___.
A) 1.00
B) 2.00
C) 0.80
D) 0.89
E) 1.09

Accepted Answer

The answer of The distribution of the number grade one...

Question 8

For a discrete uniform distribution, if a = 4 and b = 5, what is P(x=10)?
A) 0.5
B) 1.0
C) 1.5
D) -0.5
E) -1.0

Accepted Answer

The answer of For a discrete uniform distribution, if a...

Question 9

For a discrete uniform distribution, if a = 4 and b = 5, what is standard deviation?
A) 0.17
B) 0.29
C) 0.50
D) 1.00
E) 1.5

Accepted Answer

The answer of For a discrete uniform distribution, if a...

Question 10

If x is a binomial random variable with n = 10 and π = 0.8, the mean value of x is ___.
A) 6
B) 4.8
C) 3.2
D) 8
E) 48

Accepted Answer

The mean of a binomial distribution is calculated as n * π, which is 10 * 0.8 = 8.

Question 11

During a recent sporting event, a quarter is tossed to determine which team picks the starting side. Suppose the referee says the coin will be tossed 3 times and the best two out of three wins If team A calls 'heads', what is the probability that exactly two heads are observed in three tosses?
A).313
B).375
C).625
D).875
E).500

Accepted Answer

The probability of getting exactly two heads in three tosses is calculated by considering the different ways heads can occur in three tosses (HHT, HTH, THH) and the probability of each sequence. The probability of each sequence is (1/2)^3 = 1/8, since each toss is independent. There are 3 such sequences, so the total probability is 3*(1/8) = 3/8 = .375.

Question 12

The formula for the mean of a discrete uniform distribution is
A)  .
B)  .
C)  .
D)  .
E)  .

Accepted Answer

The formula for the mean of a discrete uniform distribution is (a+b)/2 where a and b are the minimum and maximum values in the distribution. Since the distribution is uniform, all values are equally likely to occur. In this case, we do not have any specific values for a and b, so we cannot provide a numerical answer. However, we can determine that choice C is the correct formula based on the format of the answer choices, which all follow a similar pattern (a,b,c,d,e).

Question 13

If x is a binomial random variable with n = 10 and π = 0.8, what is the probability that x is equal to 4?
A).0055
B).0063
C).124
D).232
E).994

Accepted Answer

The probability of x being equal to 4 in a binomial distribution can be calculated using the formula P(x=k) = C(n,k) * π^k * (1-π)^(n-k). For n=10, π=0.8, and k=4, this results in approximately 0.0055.

Question 14

A student randomly guesses the answers to a five question true/false test. If there is a 50% chance of guessing correctly on each question, what is the probability that the student misses exactly 1 question?
A) 0.200
B) 0.031
C) 0.156
D) 0.073
E) 0.001

Accepted Answer

The probability of getting exactly one question wrong is the probability of getting four questions right (0.5^4) multiplied by the probability of getting one question wrong (0.5), which is 0.5^4 * 0.5 = 0.156.

Question 15

At A-Life Corporation, managers begin at $35/hour until they reach $50/hour (salaries are always to the nearest dollar). If the variable x = hourly wage has a discrete uniform distribution, what is the probability that a manager's wage is between $42 and $45?
A) 0.50
B) 0.35
C) 0.30
D) 0.25
E) 0.13

Accepted Answer

The answer of At A-Life Corporation, managers begin at $35/hour...

Question 16

If x is a binomial random variable with n = 10 and π = 0.8, the standard deviation of x is ___.
A) 8.0
B) 1.26
C) 1.60
D) 64.0
E) 10

Accepted Answer

The formula for the standard deviation of a binomial distribution is:

σ = sqrt( n * π * (1 - π) )

Plugging in the values for n and π, we get:

σ = sqrt( 10 * 0.8 * (1 - 0.8) ) = 1.26 (rounded to two decimal places)

Question 17

If x has a binomial distribution with π =.5, then the distribution of x is ___.
A) skewed to the right
B) skewed to the left
C) symmetric
D) a Poisson distribution
E) a hypergeometric distribution

Accepted Answer

A binomial distribution with a probability of success of 0.5 is symmetric. The mean and median will be equal, and the distribution will be bell-shaped.

Question 18

A student randomly guesses the answers to a five question true/false test. If there is a 50% chance of guessing correctly on each question, what is the probability that the student misses no questions?
A) 0.000
B) 0.200
C) 0.500
D) 0.031
E) 1.000

Accepted Answer

Since there are only two options for each question, the probability of guessing all five correctly is (1/2)^5=1/32 or 0.03125. Therefore, the answer is D.

Question 19

For a discrete uniform distribution, if a = 4 and b = 5, what is the expected value?
A) 0.5
B) 4.5
C) 1.5
D) 9.0
E) 4.0

Accepted Answer

The expected value for a discrete uniform distribution is calculated as (a + b) / 2. Here, (4 + 5) / 2 = 4.5.

Question 20

The probability distribution for the daily demand of laptops at a local store is shown below. In this distribution, the random variable x is the daily demand of laptops:  Which of the following statements is true?
A) This distribution is skewed to the right.
B) This is a binomial distribution.
C) This is a normal distribution.
D) This distribution is skewed to the left.
E) This distribution is bimodal.

Accepted Answer

The distribution is not symmetrical and has a longer tail to the left, indicating that it is skewed to the left. Therefore, the correct option is D. Option A is incorrect since the skewness is towards the left, not the right. Option B is inappropriate since the binomial distributions give the probability of a certain number of successes in a fixed number of trials. Option C is inappropriate as the shape of the distribution is not bell-shaped, which is one of the characteristics of a normal distribution. Option E is also incorrect because there is only one mode, which is 25.

Quiz 7: Discrete Probability Distributions

The probability distribution for the daily demand of laptops at a local store is shown below. In this distribution, the random variable x is the daily demand of laptops: The mean (average) value of x is ___.

At A-Life Corporation, managers begin at $35/hour until they reach $50/hour (salaries are always to the nearest dollar) . If the variable x = hourly wage has a discrete uniform distribution, what is the mean wage for the managers?

The probability distribution for the daily demand of laptops at a local store is shown below. In this distribution, the random variable x is the daily demand of laptops: The standard deviation of x is ___.

At A-Life Corporation, managers begin at $35/hour until they reach $50/hour (salaries are always to the nearest dollar) . If the variable x = hourly wage has a discrete uniform distribution, what is the standard deviation of x?

The distribution of the number grade one students per household in a rural community is shown below. In this distribution, the random variable x is the number grade one students per household: The mean (average) value of x is ___.

The distribution of the number grade one students per household in a rural community is shown below. In this distribution, the random variable x is the number grade one students per household: The standard deviation of x is ___.

For a discrete uniform distribution, if a = 4 and b = 5, what is P(x=10) ?

For a discrete uniform distribution, if a = 4 and b = 5, what is standard deviation?

If x is a binomial random variable with n = 10 and π = 0.8, the mean value of x is ___.

During a recent sporting event, a quarter is tossed to determine which team picks the starting side. Suppose the referee says the coin will be tossed 3 times and the best two out of three wins If team A calls 'heads', what is the probability that exactly two heads are observed in three tosses?

The formula for the mean of a discrete uniform distribution is

If x is a binomial random variable with n = 10 and π = 0.8, what is the probability that x is equal to 4?

A student randomly guesses the answers to a five question true/false test. If there is a 50% chance of guessing correctly on each question, what is the probability that the student misses exactly 1 question?

At A-Life Corporation, managers begin at $35/hour until they reach $50/hour (salaries are always to the nearest dollar) . If the variable x = hourly wage has a discrete uniform distribution, what is the probability that a manager's wage is between $42 and $45?

If x is a binomial random variable with n = 10 and π = 0.8, the standard deviation of x is ___.

If x has a binomial distribution with π =.5, then the distribution of x is ___.

A student randomly guesses the answers to a five question true/false test. If there is a 50% chance of guessing correctly on each question, what is the probability that the student misses no questions?

For a discrete uniform distribution, if a = 4 and b = 5, what is the expected value?

The probability distribution for the daily demand of laptops at a local store is shown below. In this distribution, the random variable x is the daily demand of laptops: Which of the following statements is true?