Going to Work: The mean distance that commuters in a city travel each way to wor

Question

Going to Work: The mean distance that commuters in a city travel each way to work is 18 miles. Assume the standard deviation is 9 miles. A sample of 80 commuters is chosen. Use the TI-84 calculator to answer the following. What is the probability that the sample mean commute distance is greater than 15 miles? Round the answer to four decimal places. The probability that the sample mean commute distance is greater than 15 miles is 0.9986. What is the probability that the sample mean commute distance is between 20 and 23 miles? Round the answer to four decimal places. The probability that the sample mean compute distance is between 20 and 23 miles is

Explanation / Answer

2] the probability that the sample mean is commute distance between 20 and 23 miles.

Pr ( 20 < Xbar < 23) = Pr ( sqrt(80)*(20-18)/9 < sqrt(n)*(Xbar - mu)/sigma < sqrt(80)*(23-18)/9 )

                                = Pr ( 1.9876 < Z < 4.9690)   where Z is standard normal variate

                                = 0.0234 ( calculated by using Excel command " =NORMSDIST(4.969)-NORMSDIST(1.9876) "

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