Question

A normal distribution has a mean of 15 and a standard deviation of 2. Find the value that corresponds to the 75th percentile. Round two decimal places

Answer 1

16.35

Explanation:

Using an inverse normal distribution, we can calculate the z score given the percentile, which can then be used to find our value.

First, we can use an inverse normal distribution calculator to figure out that the z score given the 75th percentile is 0.674.

Next, we know that the z score is (observed value - mean) / standard deviation. We can plug our values in to get

`(x-15)/(2) = z\\(x-15)/(2) = 0.674\\x-15 = 0.674 * 2\\x = 0.674 * 2 + 15\\x= 16.348`

Rounding, we get x = 16.35 as our answer