Men's heights are normally distributed with mean 70.2 in and standard deviation of 2.8 in. Women's heights are normally distributed with mean 63.9 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? Click to view page 1 of the table. Click to view page 2 of the table. a. 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.) b. The statistician would design a house with doorway height ] in. (Round to the nearest tenth as needed.)Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. Click to view page 1 of the table. Click to view page 2 of the table. Q 0.97 The indicated IQ score, x, is . (Round to one decimal place as needed.)Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. Click to view page 1 of the table, Click to view page 2 of the table. 0.97 The indicated IQ score, x, is . (Round to one decimal place as needed.)