## Related questions with answers

Apolitical action group is planning to interview home owners to assess the impact caused by a recent slump in housing prices. According to a Wall Street Journal/Harris Interactive Personal Finance poll, 26% of individuals aged 18–34, 50% of individuals aged 35–44, and 88% of individuals aged 55 and over are home owners (All Business website, January 23, 2008). a. How many people from the 18–34 age group must be sampled to find an expected number of at least 20 home owners? b. How many people from the 35–44 age group must be sampled to find an expected number of at least 20 home owners? c. How many people from the 55 and over age group must be sampled to find an expected number of at least 20 home owners? d. If the number of 18–34 year olds sampled is equal to the value identified in part (a), what is the standard deviation of the number who will be home owners? e. If the number of 35–44 year olds sampled is equal to the value identified in part (b), what is the standard deviation of the number who will be home owners?

Solution

Verifieda. Given:

$p=26\%=0.26$

$E(X)=\mu=20$

The mean of a binomial distribution is the product of the sample size $n$ and the probability $p$:

$\mu=np$

Solve to $n$:

$n=\dfrac{\mu}{p}$

Fill in the known values and evaluate:

$n=\dfrac{20}{0.26}\approx 77$

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