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(e) At the mean, the height of the curve is 0.5 10. The 16th percentile of a Normally distributed variable has a value of 25 and the 97.s percentile has a value of 40. Which of the following is the best estimate of the mean and standard deviation of the variable? (a) Mean 32.5; Standard deviation 2.5 (b) Mean32.5; Standard deviation 5 (c) Mean32.5; Standard deviation 10 (d) Mean30; Standard deviation 2.5 (e) Mean30; Standard deviation 5
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Answer #1

By the 68-95-99.7 rule,
the 16th percentile is about 1 standard deviation below the mean
and the 97.5th percentile is about 2 standard deviations above the mean.
Hence the interval from 25 to 40 is three standard deviations, so the standard deviation is 5 and the mean is 25 + 5 = 30.

Option e) is correct

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