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Chapter 4: Q75E (page 247)

Museum management. Refer to the Museum Management and Curatorship (June 2010) study of the criteria used to evaluate museum performance, Exercise 3.18 (p. 170). Recall that the managers of 30 leading museums of contemporary art were asked to provide the performance measure used most often. Of these 30 museums, 8 specified 鈥渢otal visitors鈥� as the performance measure. Consider a random sample of 5 museums selected from the 30. How likely is it that none of the museums in the sample specified 鈥渢otal visitors鈥� as the performance measure?

Short Answer

Expert verified

The sample specified 鈥渢otal visitor鈥� as the performance measure is 0.184.

Step by step solution

01

 Given Information

A random sample of 5 museums selected from the 30 is given.

N=30M=8n=5

Let x be the number of times 鈥渢otal visitor鈥� is selected.

02

Hypergeometric distribution is used to solve the above problem.

Therefore,

px=0=M0脳N-Mn-0Nn=80脳30-85-0305=1脳26334142506=0.184

Hence, the sample specified 鈥渢otal visitors鈥� as the performance measure is 0.184.

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Most popular questions from this chapter

Mailrooms contaminated with anthrax. During autumn 2001, there was a highly publicized outbreak of anthrax cases among U.S. Postal Service workers. In Chance (Spring 2002), research statisticians discussed the problem of sampling mailrooms for the presence of anthrax spores. Let x equal the number of mailrooms contaminated with anthrax spores in a random sample of n mailrooms selected from a population of N mailrooms. The researchers showed that the probability distribution for x is given by the formula P(x)=(kx)(N-kn-x)(Nn)

where k is the number of contaminated mailrooms in the population. (In Section 4.4 we identify this probability distribution as the hypergeometric distribution.) Suppose N = 100, n = 3, and k = 20.

a. Find p(0).

b. Find p(1)

. c. Find p(2).

d. Find p(3)

The binomial probability distribution is a family of probability distributions with every single distribution depending on the values of n and p. Assume that x is a binomial random variable with n = 4.

  1. Determine a value of p such that the probability distribution of x is symmetric.
  2. Determine a value of p such that the probability distribution of x is skewed to the right.
  3. Determine a value of p such that the probability distribution of x is skewed to the left.
  4. Graph each of the binomial distributions you obtained in parts a, b, and c. Locate the mean for each distribution on its graph.\
  5. In general, for what values of p will a binomial distribution be symmetric? Skewed to the right? Skewed to the left?

The Apprenticecontestants鈥� performance ratings. Referto the Significance(April 2015) study of contestants鈥� performanceson the United Kingdom鈥檚 version of the TVshow, The Apprentice, Exercise 2.9 (p. 73). Recall thatthe performance of each of 159 contestants was rated ona 20-point scale. Contestants were also divided into twogroups: those who played for a job and those who playedfor a businesspartnership. These data (simulated, based onstatistics reportedin the article) are saved in the accompanyingfile. Descriptive statistics for each of the two groupsof contestants are displayed in the accompanying Minitabprintout.

a. Determine whether the performance ratings of contestantswho played for a job are approximately normallydistributed.

b. Determine whether the performance ratings of contestantswho played for a business partnership are approximatelynormally distributed.

Descriptive Statistics: Rating

Variable Rating

Price

N

Mean

St.Dev

Minimum

Q

1

median

Q3

Maximum

IQ

R

Job

99

7.879

4.224

1

4

9

11

20

7

Partner

60

8.883

4.809

1

5

8

12

20

7

Ages of 鈥渄ot-com鈥� employees. The age (in years) distribution for the employees of a highly successful 鈥渄ot-com鈥� company headquartered in Atlanta is shown in the next table. An employee is to be randomly selected from this population.

  1. Can the relative frequency distribution in the table be interpreted as a probability distribution? Explain.
  2. Graph the probability distribution.
  3. What is the probability that the randomly selected employee is over 30 years of age? Over 40 years of age? Under 30 years of age?
  4. What is the probability that the randomly selected employee will be 25 or 26 years old?

Making high-stakes insurance decisions. The Journal of Economic Psychology (September 2008) published the results of a high-stakes experiment in which subjects were asked how much they would pay for insuring a valuable painting. The painting was threatened by fire and theft, hence, the need for insurance. To make the risk realistic, the subjects were informed that if it rained on exactly 24 days in July, the painting was considered to be stolen; if it rained on exactly 23 days in August, the painting was considered to be destroyed by fire. Although the probability of these two events, 鈥渇ire鈥� and 鈥渢heft,鈥� was ambiguous for the subjects, the researchers estimated their probabilities of occurrence at .0001. Rain frequencies for the months of July and August were shown to follow a Poisson distribution with a mean of 10 days per month.

a. Find the probability that it will rain on exactly 24 days in July.

b. Find the probability that it will rain on exactly 23 days in August.

c. Are the probabilities, parts a and b, good approximations to the probabilities of 鈥渇ire鈥� and 鈥渢heft鈥�?
See all solutions

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