A) The quality control section of a purchasing contract for valves specifies that the diameter must be between 2.53 and 2.57 centimeters. Assume that the production equipment is set so that the diameter follows normal distribution with mean diameter 2.56 centimeters and the standard deviation 0.01 centimeters. What is the percent of valves produced, over the long run, will be within these specifications?

B) The chocolate chip cookies that are produced at Perry's Cookie Emporium have weights which are approximately normally distributed with the mean weight 180 grams and with standard deviations 20 grams. The cookies, however, are sold by count, not by weight. Perry wants to improve his image, so he decides to set aside lightest 20% of the cookies to be packaged and sold separately. What cookie weight will divide the lightest 20% from the heaviest 80%?

C) Bluefish purchased at the Lime Beach Fishing Terminal produce a filet weight which has a mean of 4.5 pounds with a standard deviation of 0.8 pound. If you purchase five such fish, then what is the probability that you will have at least 21 pounds of filets? Notice that in general 5 is a very small sample size to apply the Central Limit Theorem (CLT). However, the conclusion of the CLT holds even for small samples if the population distribution is normal or close to normal. Assume here that the population distribution of filet weights is close to normal.