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. What is the probability that a randomly selected Ping-Pong ball will have a diameter of:
a. Between 1.28 and 1.30 inches?
b. Between 1.31 and 1.33 inches?
c. Between what two values will 60% of the Ping-Pong balls fall (in terms of the diameter)?
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,
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).
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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).
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