Math  /  Data & Statistics

QuestionGoing to work: A news report stated that the mean distance that commuters in the United States travel each way to work is 16 miles. Assume the standard deviation is 6 miles. A sample of 75 commuters is chosen.
Part: 0/20 / 2 \square
Part 1 of 2 (a) What is the probability that the sample mean commute distance is greater than 14 miles? Round the answer to at least four decimal places.
The probability that the sample mean commute distance is greater than 14 miles is \square .

Studdy Solution
Determine the probability that the sample mean is greater than 14 miles. This is equivalent to finding P(Z>2.886) P(Z > -2.886) .
Using standard normal distribution tables or a calculator, find:
P(Z>2.886)=1P(Z<2.886) P(Z > -2.886) = 1 - P(Z < -2.886)
P(Z<2.886)0.0019 P(Z < -2.886) \approx 0.0019
Thus,
P(Z>2.886)=10.0019=0.9981 P(Z > -2.886) = 1 - 0.0019 = 0.9981
The probability that the sample mean commute distance is greater than 14 miles is 0.9981 \boxed{0.9981} .

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