The owner of a small restaurant is trying to quantify the variation in the daily demand for takeout lunches. She has decided to assume that the demand is normally distributed. She knows on average 100 takeout lunches are purchased daily and that 90% of the time, the daily demand is below 116.

a) What is the standard deviation of this distribution?

b) The owner of the restaurant wants to stock enough boxes each day so that the probability of running out of boxes is no higher than 0.05. What is the lowest number of boxes she should stock to achieve this?