A small grocery store sells fresh produce, which it obtains from a local farmer.

Question

A small grocery store sells fresh produce, which it obtains from a local farmer. During the strawberry season, demand for fresh strawberries can be reasonably approximated using a normal distribution with a mean of 42 quarts per day and a standard deviation of 8 quarts per day. Excess costs run .45 cents per quart. The grocer orders 43 quarts per day.
Use Table.
  
What is the implied cost of shortage per quart? (Round your z value to 2 decimal places, your service level probability to 4 decimal places and your final answer to 2 decimal places. Omit the "$" sign in your response.)
  
Shortage cost per quart           $

Explanation / Answer

Mean = 42

Stdev = 8

P(X <= 43) = P(Z <= 43-42/8) = P(Z <= .125) = .5495or .55 ( round off 2 decimals)

Service level = P(X<=43) = Cs / (Cs + Ce) = .55

1/.5495 = Cs/.45 + 1

Cs = (1/.5495 - 1)*.45

Cs = .3689 or $.37 rounded off to 2 decimals as asked in the question.

Shortage cost per quart : $0.37

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