Question 204718
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 inches.
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If you don't have software or a calculator you will have to do these using
z-values and a z-chart.  My answers are based on using a TI calculator.
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 What is the probability that a randomly selected Ping-Pong ball will have a diameter of: 

a. Between 1.28 and 1.30 inches?
Ans: normalcdf(1.28,1.30,1.30,0.04) = 0.1915
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b. Between 1.31 and 1.33 inches?
Ans: normalcdf(1.31,1.33,1.30,0.04) = 0.1747
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c. Between what two values will 60% of the Ping-Pong balls fall (in terms of the diameter)? 
You need the z-value that is 30% to the right and 30% to the left of the
mean.  That value is InvNorm(0.20) = 0.8416
Then you have to use x = u + z*sugma to find the correct x-values
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If random samples of 16 Ping-Pong balls were selected, 
d. What proportion of the sample means would be between 1.31 and 1.33 inches? 
If random samples of 100 Ping-Pong balls were selected,
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The standard deviation has changed to 0.04/sqrt(16) = 0.01 because of 
the Central Limit Theorem.
Ans: normalcdf(1.31,1.33,1.3,0.01) = 0.1573
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I'll leave the rest to you.
Cheers,
Stan H.
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e. What proportion of the sample means would be between 1.31 and 1.33 inches?

f. Compare your results in (b), (d) and (e).