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The average diameter of sand dollars on a certain island is 5.00 centimeters with a standard deviation of 0.90 centimeters. If 16 sand dollars are chosen at random for a collection, find the probability that the average diameter of those sand dollars is more than 4.73 centimeters. Assume that the variable is normally distributed.

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Answer:

the probability that the average diameter of those sand dollars is more than 4.73 centimeters is 0.5910

Step-by-step explanation:

Given information:

mean, x = 5

standard deviation, σ = 0.9

number of sample, n = 16

now we calculate the probability that the average diameter of those sand dollars is more than 4.73 centimeters.

P(x>4.73)  = P (z > (4.73 - x) / (σ [tex]\sqrt{n}[/tex])

                = P (z > (4.73 - 4) / (0.9 [tex]\sqrt{16}[/tex])

                = P (z > 0.203)

                = 0.5910

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