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Employed Women If 60% of all women are employed outside
Chapter 5, Problem 22CQ(choose chapter or problem)
Employed Women If 60% of all women are employed outside the home, find the probability that in a sample of 20 women,
a. Exactly 15 are employed
b. At least 10 are employed
c. At most 5 are not employed outside the home
Questions & Answers
QUESTION:
Employed Women If 60% of all women are employed outside the home, find the probability that in a sample of 20 women,
a. Exactly 15 are employed
b. At least 10 are employed
c. At most 5 are not employed outside the home
ANSWER:
Step 1 of 3
(a)
If 60% of all women are employed outside the home, we are asked to find the probability that in a sample of 20 women exactly 15 are employed.
Let \(x\) denote the number of women is employed outside the home.
We need to find \(P(X=15)\).
Using the binomial distribution, we can find the probability.
The binomial distribution
\(P(X=x)=n C x \times p^{x} \times(1-p)^{n-x}\)
We have given \(n=20\) and \(p=0.6\).
\(P(X=15)=20 C 15 \times(0.6)^{15} \times(1-0.6)^{20-15}=0.07465\)
Hence the probability that in a sample of 20 women exactly 15 are employed is 0.07465.