SOLUTION: 5. Historical production data indicate that the diameter of a ball bearing is normally distributed with a mean of 0.525 cm and a standard deviation of 0.008 cm. Suppose that a samp

Question 980292: 5. Historical production data indicate that the diameter of a ball bearing is normally distributed with a mean of 0.525 cm and a standard deviation of 0.008 cm. Suppose that a sample of 16 ball bearings are randomly selected from a very large lot. Determine the probability that the average diameter of a sampled ball bearing is greater than 0.530 cm.
a. 0.2324
b. 0.4938
c. 0.5062
d. 0.0062

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
z = (xbar - mu)/(sigma/sqrt(n))

z = (0.530 - 0.525)/(0.008/sqrt(16))

z = 2.5

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P(xbar > 0.530) = P(z > 2.5)

P(xbar > 0.530) = 1 - P(z < 2.5)

P(xbar > 0.530) = 1 - 0.99379 ... use a table

P(xbar > 0.530) = 0.00621

P(xbar > 0.530) = 0.0062

The probability is 0.0062

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