Chapter 6 Questions

A local police station receives an average 8.1 emergency telephone calls per hour. These calls are Poisson distributed. 22. The probability that the station will get nine calls in an hour is: a. 0.1256. b. 0.8744. c. 0.0408. d. 0.6918. e. 0.3082. 23. The probability that the station will get five to seven calls in an hour is: a. 0.5924. b. 0.5617. c. 0.4383. d. 0.4076. e. 0.3451. 24. The probability that the station will get at least 4 calls in an hour is: a. 0.0397. b. 0.0941. c. 0.9059. d. 0.9603. e. 0.9630.

a, e, d

A barbershop requires appointments for perms and hair cuts. Ten percent of those making appointments cancel or simply fail to show up. Next week's appointment calendar has 64 appointments. Let x be the number of missed appointments out of the 64. The probability that more than 3 cancellations and/or no-shows will occur during the next week is: a. 0.3784 b. 0.8937 c. 0.7795 d. 0.9611 e. 0.1063

b

A survey of college students taking the professional exam to be certified as public school teachers shows that 15 percent fail. On a national exam day, 12,000 students take the test. Let x denote the number who fail. The mean and standard deviation of the random variable x are, respectively: a. 1800; 1530 b. 1800; 39.11 c. 10,200; 1530 d. 10,200; 39.11 e. 1200; 35.71

b

Tornadoes for January in Kansas average 3.2 per month. The probability that in the next January there will be between 1 and 3 tornadoes (inclusive) is: a. 0.2087. b. 0.5617. c. 0.4383. d. 0.4076. e. 0.5924.

b

Which of the following is not a characteristic of a binomial experiment? a. There is a sequence of identical trials. b. Each trial results in two or more outcomes. c. The trials are independent of each other. d. Probability of success p is the same from one trial to another.

b

Which of the following is not a characteristic of the hypergeometric distribution? a. The hypergeometric distribution is similar to the binomial distribution in focusing on the number of successes in a given number of consecutive trials. b. The hypergeometric distribution is similar to the binomial distribution in the fact that the probability of success remains constant from one trail to the rest. c. The hypergeometric distribution relies on sampling without replacement. d. The hypergeometric distribution, the consecutive trials are not independent. e. All of the above are characteristics of the hypergeometric distribution.

b

Which of the following most likely represents a discrete random variable? a. Length of time between calls to an 800 number. b. The number of years completed in the military services. c. The S & P Industrial average of stock prices. d. The amount of retail sales on a given day. e. Length of time for which an apartment in a large complex remains vacant.

b

A Company manufactures women's hosiery. The company sells slightly irregular panty hose through a mail-order catalog service. If the company produces 300,000 pairs of hose per day and the probability of a pair not being irregular is 0.92, the average number that will be available for the catalog order department is: a. 22080 b. 148.59 c. 24000 d. 154.92 e. 15.49

c

A cashier at Carter's cafeteria can total an average of 2.2 trays per minute. The probability that the cashier will total exactly four trays in a minute is: a. 0.9275. b. 0.8918. c. 0.1082. d. 0.0992. e. 0.1169.

c

A new car salesperson knows that he sells cars to one customer out of 20 who enter the showroom. The probability that he will sell a car to exactly two of the next three customers is: a. 0.9939 b. 0.0075 c. 0.0071 d. 0.0851 e. 0.1354

c

Brendalee and Mohammed go to a coffee shop during their lunch break and toss a coin to see who will pay. The probability that Brendalee will pay three days in a row is: a. 0.2500 b. 0.5000 c. 0.1250 d. 0.0150 e. none of these.

c

The expected value, E(x), of a binomial probability distribution is: a. n + b. n (1 - ) c. n d. n + - 1

c

Tornadoes for January in Kansas average 3.2 per month. The probability that in the next January Kansas will experience exactly 2 tornadoes is: a. 0.7913. b. 0.4076. c. 0.2087. d. 0.1304. e. 0.2226.

c

Tornadoes for January in Kansas average 3.2 per month. The probability that in the next January at least 2 tornadoes will occur is: a. 0.9592. b. 0.0408. c. 0.8288. d. 0.1712. e. none of these.

c

Which of the following events is best described using a hypergeometric distribution? a. The number of customers entering a store during the next hour. b. The number of accidents at a particular intersection during the next month. c. The number of male jurors selected from a group of 25 individuals. d. The number of correct responses in a multiple choice exam. e. The number of heads after tossing a fair coin 10 times.

c

Which of the following is a discrete random variable? a. The average daily consumption of water in a U.S. household. b. The weight of football players in the NFL. c. The number of three-point shots completed in a college basketball game. d. The time required to drive from Dallas to Denver. e. The average daily temperature in the world.

c

Which probability distribution is appropriate when sampling is performed without replacement from a relatively small population? a. Binomial distribution b. Poisson distribution c. Hypergeometric distribution d. Normal distribution e. Exponential distribution

c

A cashier at Carter's cafeteria can total an average of 2.2 trays per minute. The probability that the cashier will total no more than three trays in a minute is: a. 0.1966. b. 0.6227. c. 0.9275. d. 0.8193.

d

As a rule of thumb, a binomial distribution for which the number of trials n is large can well be approximated by a Poisson distribution when the probability of success, pie, is: a. larger than 0.95. b. larger than 0.50. c. between 0.50 and 0.95. d. smaller than .05.

d

The variance of a binomial distribution for which n = 75 and = 0.20 is: a. 375. b. 75. c. 15. d. 12.

d

Which of the following statements are true? a. For the Poisson distribution = 3.2, the mean and standard deviation are both equal to 3.2. b. For the Poisson distribution = 3.2, the mean and variance are both equal to 3.2. c. For the Poisson distribution = 3.2, the mean is 3.2 and the standard deviation is 1.79. d. Both B and C are correct. e. All of these are correct.

d

A cashier at Carter's cafeteria can total an average of 2.2 trays per minute. The probability that the cashier will total between four and ten trays in a minute is: a. 0.9281. b. 0.8193. c. 0.1807. d. 0.3772. e. 0.0724.

e

Approximately 84% of persons age 70 to 84 live in their own household and are income-qualified for home purchases. If four persons are randomly selected from this population, the probability that exactly two of the four live in their own household and are income-qualified is: a. 0.8916 b. 0.4182 c. 0.0138 d. 0.5404 e. 0.1084

e

Which of the following is not a characteristic of a discrete probability distribution? a. The sum of the probabilities is one. b. The values of x are exhaustive. c. The value for the probability of any given x ranges from 0 to 1. d. The values of x are mutually exclusive. e. The sum of the probabilities for all possible values of x must be between 0 and 1.

e

A table, formula, or graph that shows all possible values a random variable can assume, together with their associated probabilities is referred to as: a. Discrete probability distribution b. Continuous probability distribution c. Mixed probability distribution d. Contaminated probability distribution

a

Approximately 14 percent of the population of Arizona is 65 years or older. A random sample of five persons from this population is taken. The probability that less than 2 of the 5 are 65 years or older is: a. 0.8533 b. 0.1467 c. 0.4704 d. 0.3829 e. None of these.

a

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.

a

The likelihood that someone who logs onto a particular site in a "shopping mall" on the Internet will purchase an item is 0.05 and follows the binomial distribution. If the site has 35 people accessing it in the next hour, what is the expected number of successes during this hour? a. 1.75 b. 2.5 c. 0.05 d. 12 e. 35

a

A box of chocolates contains 18 pieces, 10 of which have nuts while the remaining 8 do not. Four pieces are chosen at random. 31. What is the probability that exactly 2 pieces have nuts? a. 0.412 b. 0.564 c. 0.681 d. 0.750 e. 0.833 32. What is the probability that no more than one piece has nuts? a. 0.116 b. 0.206 c. 0.289 d. 0.444 e. 0.517 33. What is the probability that at least 3 pieces have nuts? a. 0.051 b. 0.118 c. 0.169 d. 0.242 e. 0.382

a, b, e