ST CH 5 Review

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 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

The following represents the probability distribution for the daily demand of computers at a local store. Demand Probability 0 0.1 1 0.2 2 0.3 3 0.2 4 0.2 What is the expected daily demand?

0(0.1) + 1(0.2) + 2(0.3) + 3(0.2) + 4(0.2) = 2.2

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

0.3125

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.

0.7618

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?

1 - (e^4 * -4^x )/ x! =0.2150 = 1 - POISSON.DIST(5,4,TRUE)

Random variable x has the following probability function: f(x) = x/6 for x = 1, 2, or 3 What is the expected value of x ?

1 x (1/6) + 2 x (1/6) + 3 x (1/6) = 2.333

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: x | 1 2 3 4 P(x)| .2. .4 .3 .1 What is the mean number of puzzles the subjects can be expected to complete?

1(0.2) + 2(0.4) + 3(0.3) + 4(0.1) = 2.3

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?

1-(0.75)^6 (0.25)^0 = 0.8220

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?

1-20%=0.80 .80(21,000) + 0.20(35,000) = $23,800

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?

15 x (54/100) = 8.1 total selectable x (specific group/total group)

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?

4/5 x 4/5 x 4/5 x 4/5 = 0.4096

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?

Calculate average (24 calls/60 minutes)*5 minutes= 2 Plug into formula P(x=3)=e^-2 * 2^3 / 3! =0.1804

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

Ef(x) = 1 for all values of x

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

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

Poisson Distribution = e^-4 * 4^6 / 6! = 0.1042 excel function =POISSON.DIST(6,4,FALSE)

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 satisfies the:

Poisson Probability Distribution

Which one of these variables is a discrete random variable?

The amount of unbroken eggs in a carton

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 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

The Poisson probability distribution is a:

discrete probability distribution

The binomial probability distribution is used with

discrete random variable

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

Expected value for a binomial distribution

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

probability of successes changes from trial to trial

Which of the following is a discrete random variable?

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

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

the graph of distribution always exhibits symmetry

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

there are exactly 2 outcomes possible on each trial

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.