Normal distribution with population knee heights
Given: Men have sitting knee heights that are normally distributed with mean of 22.0 in. and std dev of 1.1 in. Women have mean of 20.3 in and std dev of 1.0 in.
Question: Find min and max sitting knee heights that include at least 95% of all men and at at least 95% of all women.
What I did: I originally took the avg of the means given and the avg of std devs given and using invNorm found the min and max using .025 from either side of the curve. Min: 19.10 in and Max: 23.21 in. After testing these limits with the men's average I found that I was cutting out 20.9% of the men, so obviously I did this wrong. NOTE: I also found 95% max and min for each gender, but then didn't know what to do with this information.
What should I have done to find the answers?