7.13 Iron Hill Caf 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 major impact on the profitability of the restaurant. Suppose the average number of minutes that diners spend at a table for dinner at the Iron Hill Caf 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.

a.Using a sample size of 10 tables

b.Using a sample size of 20 tables

c.Using a sample size of 30 tables

d.Explain the difference in these probabilities

Solution:

Using a sample size of 10 tables

???? _x= 17/10= 17/(3.16)=5.38

Z10=(x -)/( o)=(100-93)/5.38=7/5.38=1.30

P( x10) = .9030

Using a sample size of 20 tables

???? _x= 17/20= 17/(4.47)=3.803

Z20=(x -)/( o)=(100-93)/3.803=7/3.803=1.840

P( x20) = .9671

Using a sample size of 30 tables

???? _x= 17/30= 17/(5.477) =3.104

Z10=(x -)/( o)=(100-93)/3.104=7/3.104=2.255

P( x30) = .9842

Is this correct??