The weight of a product is normally distributed with a of 4oz and a of 0.55oz.

a)What is the probability that a randomly selected unit from a recently manufactured batch weighs more than 3.75 ounces?

b) The company wants to classify a unit as a scrap in a maximum of 5% of the units if the weight isbelowa desired value. Determine the desired weight such that no more than 5% of the units are below it.

c) What is the probability that an average of 36 of these products weighs more than 4.5 ounces?

d) A new issue has arisen and the products will need to be thrown out if they weigh too much. The goal of the production manager now is to re-set the machines to a new mean (not the original 4 ounces) so that no more than 10% of the products to weigh more than 5.1 ounces. What should the new average weight be?

Please provide a detailed breakdown of the calculation. Thank you!