According to the US Bureau of Labor Statistics, 20% of all people 16 years of ag

Question

According to the US Bureau of Labor Statistics, 20% of all people 16 years of age or older do volunteer work. If a random sample of 400 people is taken, calculate the following: a) Describe the sample distribution of the sample proportion of people 16 years of age or older who do volunteer work when a random sample of 400 is taken. b) What is the probability that the sample proportion of people who do volunteer work is between 17% and 21%? c) What is the probability that more than 72 people (from the sample of 400) do volunteer work?

Explanation / Answer

a) here as np>=10 and n(1-p)>=10

therefore sample distribution of the sample proportion of people 16 years of age or older who do volunteer work when a random sample of 400 is taken is approximately normal with

sample proportion =0.20

and

b)

probability that the sample proportion of people who do volunteer work is between 17% and 21%:

c)

here as  more than 72 people means more than 72/400 =18% people for which :

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