The average diameter of sand dollars on a certain island is 3.50 centimeters with a standard deviation of 1.00 centimeters. If 25 sand dollars are chosen at random for a collection, find the probability that the average diameter of those sand dollars is more than 3.28 centimeters. Assume that the variable is normally distributed.
A) 0.636
B) 0.800
C) 0.364
D) 0.864

Question

Quizplus · Accepted Answer

The standard error of the mean is 1.00/sqrt(25) = 0.20. The z-score for 3.28 is (3.28 - 3.50) / 0.20 = -1.10. The probability of a z-score being greater than -1.10 is 0.864.

The Average Diameter of Sand Dollars on a Certain Island