Question

12A survey found that​ women's heights are normally distributed with mean 63.3 in. and standard deviation 2.3 in. The survey also found that​ men's heights are normally distributed with a mean 67.3 in. and standard deviation 92.9. Complete parts a through c below.

1. The percentage of women who meet the height requirement is ____
2. Find the percentage of men meeting the height requirement. _____
3. If the height requirements are changed to exclude only the tallest​ 5% of men and the shortest​ 5% of​ women, what are the new height​ requirements? _____

13. Men's heights are normally distributed with mean 68.6 in and standard deviation of 2.8 in. Women's heights are normally distributed with mean 63.3 in and standard deviation of 2.5 in. 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 through a standard doorway without​ bending? 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?

1. The percentage of men who are too tall to fit through a standard door without bending is ____%

​(Round to two decimal places as​ needed.)

The percentage of women who are too tall to fit through a standard door without bending is ____%

​(Round to two decimal places as​ needed.)

2. The statistician would design a house with doorway height ____ in.

​(Round to the nearest tenth as​ needed.)

Answer 1