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

Question 1

The standard deviation of a probability distribution is a measure of:

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

Answer 1

variability of the distribution

Question 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

Answer 2

to the right of the mean

Question 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

Answer 3

continuous distribution with two parameters

Question 4

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

Question 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.

Question 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

Question 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

Question 8

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

Question 9

The mean of a probability distribution is a measure of:

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

Question 10

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 11

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

Question 12

Which equation shows the process of standardizing?

A)
B)
C)
D)

Question 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

Question 14

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 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

Question 16

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 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

Question 18

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

Question 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

Question 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

Question 21

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

Question 22

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

Question 23

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

Question 24

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

Question 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.

Question 26

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

Question 27

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

Question 28

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

Question 29

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

Question 30

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

Question 31

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

Question 32

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

Question 33

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

Question 34

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

Question 35

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

Question 36

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

Question 37

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

Question 38

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

Question 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.

Question 40

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

Question 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?

Question 42

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

Question 43

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

Question 44

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

Question 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

Question 46

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 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

Question 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 if np > 5 and n(1-p) > 5.

Question 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.

Question 50

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

Question 51

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

Question 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

Question 53

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

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

Question 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

Question 55

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

Question 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

Question 57

The density function specifies the probability distribution of a continuous random variable.​

Question 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

Question 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

Question 60

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

Question 61

Find the probability distribution of X.

Question 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.

Question 63

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

Question 64

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

Question 65

Find P(X < 3).

Question 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?

Question 67

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

Question 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?

Question 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?

Question 70

Find P(2 X 4).

Question 71

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

Question 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?

Question 73

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

Question 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?

Question 75

What is the expected number of the new microwaves sold that will require a warranty repair in the first 90 days?

Question 76

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

Question 77

Find the mean and the variance of X.

Question 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?

Question 79

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

Question 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?