2. Taste Buds - Top Chefs: Assume the mean number of taste buds from the general population is 10,000 with a standard deviation of 850. You take a sample of 10 top chefs and nd the mean number of taste buds is 11,500. Assume that the number of taste-buds is a normally distributed variable for top chefs and assume the standard deviation for top chefs is the same as for the general population. (a) What is the point estimate for the mean number of taste buds for all top chefs? (b) Construct the 90% condence interval for the mean number of taste buds for all chefs. c Does our answer to the previous problem support the claim that to chefs have more taste buds y P a on average, than the general population. (d) Suppose you wanted to perform a similar study only this time you want a margin of error less than 300 at the 99% condence level. How many top chefs would you have to sample? (e) Give two reasons why your answer to the previous problem was so much larger than the original sample size of 10