My sisiter-in-law manages a tim hortons coffee shop. According to her, the number of cups of coffee sold every day is normally distributed with mean =7000 and standard deviation = 750.

a) calculate (to 5 decimal places of accuracy) both the exact and approximate (using the central limit theorem) probability that over the next 45 days, the number of days in which more than 8000 cups are sold is (strictly) fewer than 7.

b) the average sales for a 5-day period are calculated. What is the probability that this 5 day average will exceed 8000 cups?

c) Find a constant a such that there is a 75% chance that the average sales for a 5-day period will fall in the interval (-a, +a).

Thanks!