You operate a restaurant. You read that a sample survey by the National Restaurant Association shows that 30% of adults are committed to eating nutritious food when eating away from home. To help plan your menu, you decide to conduct a sample survey in your own area. You will use random digit dialing to contact an SRS of 220 households by telephone.
(a) If the national result holds in your area, is it reasonable to use the binomial distribution with n = 220 and p = 0.30 to describe the count X of respondents who seek nutritious food when eating out? Explain why.
Yes; the binomial conditions are not met but the law of large numbers says we can still use this distribution.
No; the binomial conditions are met but the sample size is small compared to the population size.
No; the binomial conditions are not met and the sample size is small compared to the population size.
Yes; the binomial conditions are met and the sample size is small compared to the population size.
(b) What is the mean number of nutrition-conscious people in your sample if p = 0.30 is true?
What is the standard deviation?
(c) What is the probability that X lies between 61 and 71? Make sure that the rule of thumb conditions are satisfied, and then use a normal approximation to answer the question.