Chapter 5: Managerial Statistics

In the textile industry, a manufacturer is interested in the number of blemishes or flaws occurring in each 100 feet of material. The probability distribution that models this situation is the:

Poisson distribution.

Find the probability that a family of five children will have exactly three boys.

.3125

The expected value for a binomial distribution is:

np

The variance Var(x) for the binomial distribution is:

np(1 − p).

The key difference between the binomial and hypergeometric distribution is that with the hypergeometric distribution:

the probability of success changes from trial to trial.

Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume X has a bell-shaped distribution with a mean of $360 and standard deviation of $50. What is the expected value and standard deviation, respectively, of the profits that the store makes in a seven-day period?

$2,520 and $132.29

The average annual incomes of high school and college graduates in a midwestern town are $21,000 and $35,000, respectively. If a company hires only personnel with at least a high school diploma and 20% of its employees have been through college, what is the mean income of the company employees?

$23,800

An insurance company charges $800 annually for car insurance. The policy specifies that the company will pay $1000 for a minor accident and $5000 for a major accident. If the probability of a motorist having a minor accident during the year is 0.2 and having a major accident is 0.05, how much can the insurance company expect to make on the policy? (Expected profit)

$350

Four percent of the customers of a mortgage company default on their payments. A sample of five customers is selected. What is the probability that exactly two customers in the sample will default on their payments?

.0142

Consider the following probability graph for a random variable x. Which of the following probability distributions corresponds to the graph? (see graph 1)

.1 .25 .3 .2 .15

The accident rate in a factory is 4 per month. What is the probability that there will be 6 accidents in a particular month?

.1042

There are 13 Democrats, 12 Republicans, and 8 Independents sitting in a room. Eight of these people will be selected to serve on a special committee. What is the probability that exactly five of the committee members will be Democrats?

.10567

The telephone sales department of a certain store receives an average of 24 calls per hour. What is the probability that between 10:00 a.m. and 10:05 a.m. there will be 3 calls?

.1804

A department store has determined in connection with its inventory control that the demand for a certain CD player averages 4 per day. If the store stocks 5 of these items on a particular day, what is the probability that demand will exceed supply?

.2150

A medicine is known to produce side effects for 1 in 5 patients taking it. Suppose a doctor prescribes the medicine to 4 unrelated patients. What is the probability that none of the patients will develop side effects?

.4096

The primary air exchange system on a proposed spacecraft has four separate components (call them A, B, C, and D) that all must work properly for the system to operate well. Assume that the probability of any one component working is independent of the other components. It has been shown that the probabilities of each component working are P(A) = 0.95, P(B) = 0.90, P(C) = 0.99, and P(D) = 0.90. Find the probability that the entire system works properly.

.7618

Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume X has a bell-shaped distribution with a mean of $360 and standard deviation of $50. What is the z-score that corresponds to the likelihood of the profit of $400?

.80

If the probability of a basketball player scoring on any shot is .75, what is the probability that she will score on at most 5 of her next 6 shots?

.8220

The primary air exchange system on a proposed spacecraft has four separate components (call them A, B, C, and D) that all must work properly for the system to operate well. Assume that the probability of any one component working is independent of the other components. It has been shown that the probabilities of each component working are P(A) = .95, P(B) = .90, P(C) = .99, and P(D) = .90. What is the probability that at least one of the four components will work properly?

.999995

Roth is a computer-consulting firm. The number of new clients that the firm has obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below. (use image 2) What is the variance of the number of new clients?

2.048

The following represents the probability distribution for the daily demand of computers at a local store. Demand / Probability0 / .11 / .22 / .33 / .24 / .2What is the expected daily demand?

2.2

A psychologist studied the number of puzzles that subjects were able to solve in a 5-minute period while listening to soothing music. Let x = the number of puzzles completed successfully by a subject. The psychologist found that x had the following probability distribution: (see image 1) What is the mean number of puzzles the subjects can be expected to complete?

2.3

Random variable x has the following probability function: see image 3 What is the expected value of x ?

2.33

Roth is a computer-consulting firm. The number of new clients that the firm has obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below. (image 2) What is the expected number of new clients per month?

3.05

The U.S. Senate has 100 members. Suppose there are 54 Republicans and 46 Democrats. A committee of 15 senators is selected at random. What is the expected number of Republicans on this committee?

8.1

Which of the following is a required condition for a discrete probability function?

Ef(x)= 1 for all values of x.

The probability distribution below represents the random variable , the length of long-distance calls in minutes in a population. x: 5 10 15 20 25P(x): .1 .2 .3 ? .1 What is the probability that the long-distance call last at least 20 minutes?

P(x)=.40

When dealing with the number of occurrences of an event over a specified interval of time or space, the appropriate probability distribution is a:

Poisson distribution.

The random variable x is the number of occurrences of an event over an interval of 10 minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in 10 minutes is 5.3. The random variable x satisfies the:

Poisson probability distribution.

The random variable x is the number of occurrences of an event over an interval of 10 minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in 10 minutes is 5.3. The appropriate probability distribution for the random variable is:

discrete.

A discrete uniform probability distribution is one where

each possible value of the random variable is the same

A measure of the central location of a random variable is called a(n):

expected value.

To compute the probability that in a random sample of n elements—selected without replacement—we will obtain x successes, we would use the:

hypergeometric probability distribution.

Which of the following is not true of discrete probability distributions?

The graph of the distribution always exhibits symmetry.

Which of the following is a discrete random variable?

The number of times a student guesses the answers to questions on a certain test

Which one of these variables is a continuous random variable?

The time it takes a randomly selected student to complete an exam

Which of the following is not a characteristic of an experiment where the binomial probability distribution is applicable?

The trials are dependent upon one another.

The binomial probability distribution is used with:

a discrete random variable.

A continuous random variable may assume:

any numerical value in an interval or collection of intervals.

An experiment consists of determining the speed of automobiles on a highway using a radar equipment. The random variable in this experiment is a:

continuous random variable.

The Poisson probability distribution is a:

discrete probability distribution.

Which one of these variables is a discrete random variable?

The number of unbroken eggs in a carton

Which of the following is a characteristic of an experiment where the binomial probability distribution is applicable?

There are exactly two outcomes possible on each trial.