Two questions that have me stumped!

1. Assume that adults have IQ scores that normally distribute with a mean of 100 and a standard deviation of 20. Find P15, which is the IQ score separating the bottom 15% from the top 85%.

-At first, I thought I would have to plug in the answers to find the mean, but obviously not. Lol


2. Men's heights are normally distributed with a mean of 68.9in and standard deviation of 2.8in. Women's heights are normally distributed with mean 63.8in and standard deviation of 2.5in. The standard doorway height is 80 in.
a. What percentage of men are too tall to fit through a standard doorway without bending, and what percentage of women are too tall to fit?
b. If a statistician designs a house so that all of the doorways have heights that are sufficient for all men except the tallest 5%, what doorway height would be used?

-This one just totally lost me.


Thanks so much for your time!

n = # of standard deviations to split 15% to the left and 85% to the right. Note, that this will be less than 100.

\(\displaystyle Z_{0.15} = \frac{n-100}{20}\)