Agricultural scientists are working on developing an improved variety of a breed of tomatoes. Marketing research indicates that customers are likely to bypass tomatoes that weigh less than 74 grams. The current variety of tomatoes produces fruit that averages 77 grams, but 10% of the tomatoes are too small. It is reasonable to assume that a normal model applies. a) What is the standard deviation of the weights of tomatoes now being grown? (Round to two decimal places.) __________ b) Scientists hope to reduce the frequency of undersized tomatoes to no more than 3%. One way to accomplish this is to raise the average size of the fruit. If the standard deviation remains the same as in part a, what target mean should they have as a goal? (Round to two decimal places.) __________ c) The researchers produce a new variety with a mean weight of 67 grams, which meets the 3% goal. What is the standard deviation of the weights of these new tomatoes? (Round to two decimal places.)