SOLUTION: 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

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Question 353663: 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?

Found 2 solutions by stanbon, jrfrunner:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
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?
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z(40) = (40-35)/8 = 0.6250
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P(x > 40) = P(z > 0.6250) = 0.2660
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b) How many loaves should the bakery make each day so that they can meet the demand 90% of the time?
Find the z-value with a left tail of 90%
invNorm(0.9) = 1.2816
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Find the corresponding x value:
x = 1.2816*8+35 = 45.25 loaves
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c) What is the probability of exceeding 38 loaves, given that the demand exceeds????
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Cheers,
Stan H.

Answer by jrfrunner(365) (Show Source):
You can put this solution on YOUR website!
c) What is the probability of exceeding 38 loaves, given that the demand exceeds 35?
P(X>38/x>35)=P(X>38 and X>35)/P(X>35)
=P(X>38)/P(X>35)
=P(Z>(38-35)/8)/P(Z>0)
=P(Z>0.375)/P(Z>0)
=0.354/0.5=0.708