You are the new owner of a restaurant. You read that a sample survey by the National Restaurant Association shows that 40% 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 200 households by telephone.
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a) If the national result holds in your area, is it reasonable to use a normal approximation for the sampling distribution? Be sure to justify your response.
b) What is the mean number of nutrition-conscious people in your sample if p = 0:4 is true?
c) What is the probability that X lies between 75 and 85?
d) You found that 100 of your 200 respondents are concerned about nutrition. Is this reason to believe that the percent in your area is higher than the national 40%?