2. During this past holiday season, there was a cheesecake craze followed by a cream cheese shortage. Assume the population for the amount of cream cheese packages required for a typical cheesecake recipe follows a normal distribution x~N(3, 1).

a. What is the probability 8 home bakers each used less than 4 packages of cream cheese for a single cheesecake recipe?

b. What is the probability the total number of cream cheese packages used for 30 cheesecake recipes exceeded 87?

c. Construct a 95% confidence interval for the number of cream cheese packages used for two cheesecake recipes. Interpret the interval.