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Quantitative Analysis - diameter of Ping-Pong balls

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The diameter of Ping-Pong balls manufactured at a large factory is expected to be approximately normally distributed with a mean of 1.30 inches and a standard deviation of 0.04 inch. What is the probability that a randomly selected Ping-Pong ball will have a diameter...
a. less than 1.28 inches?
b. Between 1.31 and 1.33 inches?
c. Between what two values (symmetrically distributed around the mean) will 60% of the Ping-Pong balls fall (in terms of diameter)?

If many random samples of 16 Ping-Pong balls were selected...

d. What will be the values of the population mean and standard error of the mean?
e. What distribution will the sample means follow?
f. What proportion of the sample means will be less than 1.28 inches?
g. What proportion of the sample means will be between 1.31 and 1.33 inches?
h. Between what two values symmetrically distributed around the mean will 60% of the sample means be?
i. Compare the answers of (a) with (f) and (b) with (g). Provide a detailed explanation accordingly.
j. Explain the difference in the results of (c) and (h).
k. Which is more likely to occur - an individual ball above 1.34 inches, a sample mean above 1.32 inches in a sample of size 4, or a sample mean above 1.31 inches in a sample of size 16? Explain.

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The solution finds the probability of randomly selecting ping-pong balls with different diameters. The distribution of sizes are determined.

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