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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 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⩾1=1-px=0=1-0.943=0.057

Therefore, the probability is 0.057.

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