Solve the problem.
-Among a random sample of 500 college students, the mean number of hours worked per week at non-college related jobs is 15.1. This mean lies 2.8 standard deviation(s)below the mean of the sampling distribution. If a second sample of 500 students is selected, what is the probability that for the second sample, the mean number oOf hours worked will be at least 15.1?
A)0.0026
B)0.9974
C)0.5
D)0.9965

Question

Quizplus · Accepted Answer

The mean of 15.1 hours being 2.8 standard deviations below the mean of the sampling distribution indicates it's on the left tail of the normal distribution curve. Since normal distribution is symmetric, the probability of a sample mean being at least 15.1 hours (i.e., equal to or greater than this value) covers the right half of the distribution plus the left tail up to 15.1 hours. This area corresponds to 50% of the distribution (right half) plus the area to the left of 15.1 hours, which is very close to the entire distribution since 15.1 is far left. Thus, the probability is very high, close to 1, making 0.9974 the correct choice.

Solve the Problem. -Among a Random Sample of 500 College Students, the Mean