Find the percentile

Question

Normally distributed with a mean of 258 feet and a standard deviation of 56 feet. We randomly sample 49 baseballs.

Find the 80th percentile of the distribution of the average 0f 49 baseballs. (round your answer to two decimal places.)

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Answer 1

First, use Table A (Z-scores) to find the area that is closest to 0.8. The z-score for the 80th percentile is 0.84.

You could also use a TI-84 calculator to find this. Use InvNorm(0.8, 0, 1, LEFT) = 0.84

Then, solve the equation: 0.84 = (x - 258)/56

Multiply both sides by 56: 47.04 = x - 258

add 258 to both sides x = 305.04

The 80th percentile is about 305 feet