SOLUTION: The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that the average height of a samp
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Question 647891: The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that the average height of a sample of ten 18-year-old men will be between 69 and 71 inches?
Answer
a. 0.8539
b. 0.2922
c. 0.3539
d. 0.1461
e. 0.1611
If you could please show me how to solve this problem. Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that the average height of a sample of ten 18-year-old men will be between 69 and 71 inches?
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Note: The mean of the sample means is 68
The standard deviation of the sample means is 3/sqrt(10)
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z(69) = (69-68)/(3/sqrt(10)) = 1.0541
z(71) = (71-68)/(3/sqrt(10)) = 3.1623
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P(69 < x-bar < 71) = P(1.0541 < z < 3.1623) = 0.1451
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Cheers,
Stan H.
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Answer
a. 0.8539
b. 0.2922
c. 0.3539
d. 0.1461
e. 0.1611
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