SOLUTION: Assume that women have heights that are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. Find the value of quartile 3. (Round to the nearest

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Question 1205166: Assume that women have heights that are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. Find the value of quartile 3. (Round to the nearest whole number.)
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
mean is 63.6
standard deviation is 2.5

at quartile 3, 75% of the values are less than that.

z-score formula is z = (x-m)/s

z is the z-score
x is the raw score
m is the raw mean
s is the stqandard deviation

formula becomes z = (x - 63.6) / 2.5

z-score with 75% of the area under the normal distribution curve to the left of it is equal to .67449 rounded to 5 decimal places.

when z = that, z-score formula becomes .67449 = (x - 63.6) / 2.5
solve for x to get x = 2.5 * .67449 + 63.6 = 65.286225.
round to 2 decimal places to get 65.29.

65.29 is the score that is at the 75th percentile of the data set which is at quartile 3.

here's what it looks like on a normal distribution calculator.
first display is with z-scores.
second display is with raw scores.