How do I find the range of lengths in this question?

The length of a Daschund is normally distributed with a mean of 15 inches, and a standard deviation of 3.5 inches. What range of lengths would occur 75% of the time?

My main issue is that I don't know how to find the z scores in the context of this question.

1 Answer
Jun 26, 2018

The range would be 15+-4.025, ie (10.975, 19.025)

Explanation:

75% of the time is 0.75/2 = 0.375

Looking at the standard normal table below, this corresponds to the Z value of 1.15 (the exact area under the curve in the table is 0.3749).

Therefore,

Z = (X - "mean")/(SD) = (X - 15)/(3.5)

Solving for X

X = "mean" +- 4.025

= 15 +- 4.025.

http://thinkpawsitive.co/z-table-chart/http://thinkpawsitive.co/z-table-chart/