The average diameter of sand dollars on a certain island is

The average diameter of sand dollars on a certain island is 4.50 centimeters with a standard deviation of 0.80 centimeters. If 9 sand dollars are chosen at random for a collection, find the probability that the average diameter of those sand dollars is more than 4.260 centimeters. Assume that the variable is normally distributed.

Solution

1. First compute the z-statistic. (x - ?)/(?/sqrt(N)) where x = test value = 4.197 cm, ? = 4.5 cm, N = 9, ? = 0.70. You get -1.298

2. You need to find the probability that the sample mean > 4.197 cm. Looking up the z-score, you get 0.0968 for sample mean < 4.197 cm. Thus, required value = 1 - 0.0968 = 0.9032