How many loaves should the bakery make each day so that they can meet the demand 90% of the time?

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December 25, 2020
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A bakery shop sells loaves of fresh French bread. Any unsold loaves at the end of the day are either discarded or sold elsewhere at a loss. The demand for this bread has followed a normal distribution with mu = 35 loaves and sigma = 8 loaves.
a)If 40 loaves are to be made each day, what is the probability of not meeting demand?
b)How many loaves should the bakery make each day so that they can meet the demand 90% of the time?
c)What is the probability of exceeding 38 loaves, given that the demand exceeds 35?