SOLUTION: A recent study by the Island Resort Taxi Drivers Association showed that the mean fare charged for service from the beach to the airport is $21.00 and the standard deviation is $3.

Question 1070821: A recent study by the Island Resort Taxi Drivers Association showed that the mean fare charged for service from the beach to the airport is $21.00 and the standard deviation is $3.50. We select a sample of 15 fares.
a. What is the likelihood that the sample mean is between $20.00 and $23.00?
b. What must you assume to make the above calculation?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A recent study by the Island Resort Taxi Drivers Association showed that the mean fare charged for service from the beach to the airport is $21.00 and the standard deviation is $3.50. We select a sample of 15 fares.
a. What is the likelihood that the sample mean is between $20.00 and $23.00?
z(20) = (20-21)/[3.5/sqrt(15)] = -1.1066
z(23) = (23-21)/[3.5/sqrt(15)] = 2.2131
P(20 < x-bar < 23) = P(-1.1066 < z < 2.2131)
= normalcdf(1.1066,2.2131) = 0.8522
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b. What must you assume to make the above calculation?
The distribution approaches a normal distribution
as sample size increases.
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Cheers,
Stan H.
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