Answer all questions with detailed explanation

A random customer's utility of consuming a bakery sample is normally distributed as U_i~N(1.6, 4.2), where is the customer i's utility, which has normal distribution with mean 1.6 and variance 4.2.

If the customer's utility is positive, she will buy the bakery (food). Otherwise, she will not buy.

(a) What is the customer's probability of buying the new bakery? Namely, (>0)P(Ui>0).

(b) What is the probability that 3 independently visiting customers all choose to buy this new bakery?

(c) A crazy but talented baker changed the recipe to increase the utility's mean by 1, but also double its variance. Can this new recipe increase the purchasing probability?

Please provide explanation