SOLUTION: The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.63 inches and a standard deviation of 0.03 inch. If you select a random sample of ni

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Question 1195186: The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.63 inches and a standard deviation of 0.03 inch. If you select a random sample of nine tennis balls,
a. what is the sampling distribution of the mean?
b. what is the probability that the sample mean is less than 2.61 inches?
c. what is the probability that the sample mean is between 2.62 and 2.64 inches?
d. The probability is 60% that the sample mean will be between what two values symmetrically distributed around the population mean?
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
The mean of the sampling distribution of n=9 is still 2.63 inches. The sd is 0.03/sqrt(9) or 0.01 inch.
The probability of the sample mean < 2.61 inches is (2.61-2.63)/0.01=z and z <=-2. This has probability of 0.0228.
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Between 2.62 and 2.64 inches is z between -1 and +1 with probability of 0.6836
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z(0.2)=-0.8416 and z(0.8)=0.8416
so z=(x-mean)/sd
0.8416=(x-2.63)/0.01
0.08416=x-2.63
x=2.638 inches for the upper limit
x=2.546 inches for the lower limit
Those two values enclose the sample mean symmetrically.