Solve the problem.
-Among a random sample of 150 employees of a particular company, the mean commute distance is 26.8 miles. This mean lies 2.7 standard deviation(s)below the mean of the sampling distribution. If a second sample of 150 employees is selected, what is the probability that for the second sample, the mean commute
Distance will be at least 26.8 miles?
A)0.0035
B)0.9965
C)0.5
D)0.0026

Question

Quizplus · Accepted Answer

The mean of the second sample being at least 26.8 miles corresponds to the probability of observing a value greater than or equal to the observed mean in the first sample. Since the first sample's mean is 2.7 standard deviations below the mean of the sampling distribution, this places it in the lower tail of the distribution. The probability of observing a value in the upper tail (which includes the mean and values above it) is the complement of the lower tail probability. Given the symmetry of the normal distribution, if a value is 2.7 standard deviations below the mean, the probability of observing a value at least as extreme in the opposite direction (above the mean) is 1 - 0.0035 (the approximate probability associated with 2.7 standard deviations from the mean in a normal distribution), which equals 0.9965.

Solve the Problem. -Among a Random Sample of 150 Employees of a Particular