Apex company is one of the main producers of Nutrition bars in Australia. The Production manager of Apex company has reported that the weight of each Nutrition bar is a normally distributed random variable with a mean of 31.7g and a standard deviation of 0.3g.

Questions:

a. Find the probability that, if a customer buys a pack of four bars, the mean weight of the four bars will be greater than 31.4g.

b. Find the probability that, if a customer buys a pack of four bars, the mean weight of the four bars will be between 31.4g and 31.9g.