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. (a) If the national result holds in your area, it is reasonable to use the B(200, 0.4) distribution to describe the count X of respondents who seek nutritious food when eating out. Explain why. (b) What is the mean number of nutrition-conscious people in your sample if p = 0.4 is true? What is the probability that X lies between 75 and 85? (c) You nd 100 of your 200 respondents concerned about nutrition. Is this reason to believe that the percent in your area is higher than the national 40%?