Iron Hill Café is a full-service restaurant in Columbus, Ohio, which is owned an

Question

Iron Hill Café is a full-service restaurant in Columbus, Ohio, which is owned and managed by John Stevens. The number of minutes that diners spend at the table has a major impact on the profitability of the restaurant. Sup pose the average number of minutes that diners spend at a table for dinner at the Iron Hill Café is 93 minutes with a standard deviation of 17 minutes. Assume the number of minutes diners spend at their table follows the normal probability distribution. Calculate the probability that the average number of minutes that diners spend at their table for dinner will be less than 100 minutes 7.13

Explanation / Answer

A) P(X < 100) = P((X - mean)/(SD/(sqrt (n)) < (100 - 93)/(17/sqrt (10))

= P(Z < 1.30) = 0.9032

B) P(X < 100) = P((X - mean)/(SD/(sqrt (n)) < (100 - 93)/(17/sqrt (20))

= P(Z < 1.84) = 0.9671

C) P(X < 100) = ((X - mean)/(SD/(sqrt (n)) < (100 - 93)/(17/sqrt (30))

= P(Z < 2.26) = 0.9881

D) As n increase probability value also increases.

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