Suppose there are two cafes that are roughly the same distance to your morning class and you want to buy breakfast before class starts. However, during the morning rush, the waiting time from the time you get in line until the time you get your order at Cafe A is normally distributed with a mean of 28.0 minutes and a standard deviation of 4.2 minutes. Similarly, the wait at Cafe B is normally distributed with a mean of 26.9 minutes and a standard deviation of 6.1 minutes.

Please answer to three decimal places. Make sure to sketch the normal model, shade the regions of interest and explain your steps.

(a) If you can afford to wait at a cafe for up to 30 minutes before you are late to class, which cafe should you choose to go to so that you have the best chance making it to class on time? Justify your answer.

(b) If you go to cafe B during the morning rush, 95% of the time you'd be waiting between how many minutes to get your order?

(c) Suppose cafe A has recently opened an express line for beverage orders only. The waiting time from the time you get in the express line until the time you get your drink order is normally distributed with a mean of 13.2 minutes and an unknown standard deviation . If 84% of the time you wait less than 16.2 minutes, what is the value of the standard deviation?