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Chapter 4: Q72E (page 247)

Male nannies. According to the International Nanny Association (INA), 4,176 nannies were placed in a job during a recent year (www.nanny.org). Of these, only 24 were men. In Exercise 3.12 (p. 169) you found the probability that a randomly selected nanny who was placed during a recent year is a man. Now use the hypergeometric distribution to find the probability that in a random sample of 10 nannies who were placed during a recent year, at least 1 is a man

Short Answer

Expert verified

The probability that among 10 nannies were placed, at least 1 is a man is 0.057.

Step by step solution

01

Given Information

The total number of nannies were placed in a job is

N = 4176

Number of men nannies is

M = 24

The sample size is n = 10

02

To find the probability of male nanny

pmale鈥�nanny=MN=244176=0.0057

Therefore, the probability of male nanny is 0.0057.

03

Compute the probability

A minimum of two steps are required.

Here, we use hypergeometric distribution to finding the probability,

px=0=2404176-2410-0417610=240415210417610=0.943

To get the required probability,

px猢�1=1-px=0=1-0.943=0.057

Therefore, the probability is 0.057.

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Most popular questions from this chapter

Mean shifts on a production line. Six Sigma is a comprehensive approach to quality goal setting that involves statistics. An article in Aircraft Engineering and Aerospace Technology (Vol. 76, No. 6, 2004) demonstrated the use of the normal distribution in Six Sigma goal setting at Motorola Corporation. Motorola discovered that the average defect rate for parts produced on an assembly line varies from run to run and is approximately normally distributed with a mean equal to 3 defects per million. Assume that the goal at Motorola is for the average defect rate to vary no more than 1.5 standard deviations above or below the mean of 3. How likely is it that the goal will be met?

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Privacy and information sharing. Refer to the Pew Internet & American Life Project Survey (January 2016), Exercise 4.48 (p. 239). The survey revealed that half of all U.S. adults would agree to participate in a free cost-saving loyalty card program at a grocery store, even if the store could potentially sell these data on the customer鈥檚 shopping habits to third parties. In a random sample of 250 U.S. adults, let x be the number who would participate in the free loyalty card program.

a. Find the mean of x. (This value should agree with your answer to Exercise 4.48c.)

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Investment risk analysis. The risk of a portfolio of financial assets is sometimes called investment risk. In general, investment risk is typically measured by computing the variance or standard deviation of the probability distribution that describes the decision maker鈥檚 potential outcomes (gains or losses). The greater the variation in potential outcomes, the greater the uncertainty faced by the decision maker; the smaller the variation in potential outcomes, the more predictable the decision maker鈥檚 gains or losses. The two discrete probability distributions given in the next table were developed from historical data. They describe the potential total physical damage losses next year to the fleets of delivery trucks of two different firms.

Firm A




Firm B



Loss Next Year

Probabiity


Loss Next Year

Probability

0

0.01



0

0


500

0.01



200

0.01


1000

0.01



700

0.02


1500

0.02



1200

0.02


2000

0.35



1700

0.15


2500

0.3



2200

0.3


3000

0.25



2700

0.3


3500

0.02



3200

0.15


4000

0.01



3700

0.02


4500

0.01



4200

0.02


5000

0.01



4700

0.01


a. Verify that both firms have the same expected total physical damage loss.

b. Compute the standard deviation of each probability distribution and determine which firm faces the greater risk of physical damage to its fleet next year.
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