The mean attention span for adults in a certain village is 15 minutes with a standard deviation of 6.4. What is the probability of randomly selecting a sample of 30 scores from this population that has a mean attention span equal to or greater than 17 minutes?
A) 0.3783
B) 0.0436
C) 0.0446
D) 0.4564

Question

Quizplus · Accepted Answer

We can use the central limit theorem since the sample size is greater than 30. The standardized score for a sample mean of 17 minutes is z = (17-15)/(6.4/sqrt(30)) = 2.97. The probability of getting a sample mean of 17 minutes or greater is equivalent to the probability of getting a standardized score of 2.97 or greater, which is 0.0033. Using a z-table, we can find the area to the right of z=2.97, which is approximately 0.0216. However, since we are interested in a one-tailed test (equal to or greater than 17 minutes), we need to double this probability to get 0.0436. Therefore, the answer is B.

The Mean Attention Span for Adults in a Certain Village