The mean distance that commuters in a city travel each way to work is 24 miles A

Question

The mean distance that commuters in a city travel each way to work is 24 miles Assume the standard deviation is 13 miles. A sample of 76 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 20 miles? Round the answer to four decimal places. The probability that the sample mean commute distance is greater than 20 miles is 0.9963. What is the probability that the sample mean commute distance is between 26 and 28 miles? Round the answer to four decimal places. The probability that the sample mean commute distance is between 26 and 28 miles is 0.0583. Find the 55th percentile of the sample mean. Round the answer to two decimal places. The 55th percentile of the sample mean is miles.

Explanation / Answer

Stdev= 13
Mean = 24
n=76

1. P(X>20) = P(Z> (20-24)/(13/(sqrt(76)) = P(Z>-2.68) = .9963

2. P(26<X<28) = P(1.3412<Z<2.68) = .9963-.91= .0863

3. The 55th percenitle of sample mean= ? P(X<x) = .55

So, (X-24)/(13/(sqrt(76)) = .125
X = 24+.125/(13/(sqrt(76))
X = 24.084

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