Answer to Question #251293 in Statistics and Probability for tinnn

Question

The net weight of cereal produced by Lucky Charms Ltd is normally distributed with a mean of 30 ounces and a standard deviation of 0.03 ounces. A box of cereal passes the quality test if its net weight is at least 29.94 ounces.

(a) Find the probability that a box of cereal randomly selected passes the quality test.

(b) A manager of Lucky Charms Ltd selects randomly n boxes of cereal for the quality test. He expects that the probability of no more than 20 boxes of cereal failing the

quality test is at least 0.95. What is the maximum number of boxes of cereal that he would select for the quality test? Justify the method that you use in the calculation.