American Expresso sells coffee and assorted pastries. A manager at a particular

Question

American Expresso sells coffee and assorted pastries. A manager at a particular coffee stand has noticed that muffins contribute a substantial amount to the costs of running that stand. She wants to make sure that the stand is selling enough muffins to justify their continued existence at the stand. Ideally, the manager would like to sell at least 120 muffins each day. However, she notices that on far too many days this condition is not being met. Some research has shown that the average number of muffins sold each day is 92, and the standard deviation in the number of muffins sold is 23. You may find this standard normal table useful throughout the following questions. a)Calculate the percentage of days on which the coffee stand sells less than the ideal number of muffins. Give your answer as a percentage to 1 decimal place. Percentage of 'failure' days = % b)The manager is not happy with this at all. She would like to have no more than 2.5% of days being failures. However, at the moment the manager can't do anything about the average number of muffins sold and the standard deviaiton in muffins sold. Her only option is to try and lower costs, to change the limit of what is considered a 'failure'. Calculate the number x such that the following statement is true: 'The coffee stand sells less than x muffins on 2.5% of days or less.' x =

Explanation / Answer

a)Percentage of 'failure' days =P(X<120)=P(Z<(120-92)/23)=P(Z<1.22)=88.9%

b)

hre for 2.5 percentile critical z=-1.96

therefore corresponding value =mean +z*std deviation=92-1.96*23=46.92

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