According a news report the mean distance that commuters in

According a news report, the mean distance that commuters in the United States travel each way to work is 16 miles and the standard deviation is 8 miles. Assume that the distribution of these distances is relatively normal. A random sample of 75 commuters is drawn to study.

1. Is the sampling distribution normal? Why? What is the mean and what is the standard deviation of this sampling distribution.

2. What is the probability that a randomly selected commuter travels a distance of greater than 13 miles a day?

Solution

1)

yes it is because the mean distance and standard deviation come from a relatively normal

sampling distribution

mean = 16

Standard deviation = 8 / srqt (75) = 0.9238

2)

P( x > 13)

P( z > 13-16 / (8) ) =P( z > -0.38)= 1-0.3520 = 0.648