Question 2. Men's heights are normally distributed with mean 68.5 in, and standard deviation of 2.8 in. Women's heights are normally distributed with mean 63.1 in. and standard deviation of 2.5 in. The standard doorway height is 80 in. Answer these questions. Round to 2 decimal places as needed, Use the Standard Normal Table, A-2. (Do not use StatCrunch). a) What percentage of men are too tall to fit through a b) What percentage of women are too tall to fit standard doorway without bending? Answer this by going through a standard doorway without bending? Answer through the following: this by going through the following: Draw a normal curve. Label the given values of x Draw a normal curve. Label the given values of and u for men. Then shade the appropriate region x and u for women. Then shade the appropriate for men that are too tall. region needed. Using the fact that z = ", draw a standard normal Using the fact that z = *-4, draw a standard curve corresponding to the result in part a)(i). normal curve corresponding to the result in part b(i). ili. Based on your results in part (i) or (ii), use a normal E distribution table to find the percentage of men who Based on your results in part (i) or (ii), use a are too tall to fit through the standard doorway normal distribution table to find the percentage without bending. of women who are too tall to fit through the standard doorway without bending. What percentage of women will have a height If a statistician designs a house so that all of the between 67 in and 80 in? Make sure to draw the normal doorways have heights that are sufficient for all curve and shade the region corresponding to the height men except the tallest 5%, what doorway height between 67 in and 80 in. would be used? Answer this by going through the following: Draw a normal curve and shade the area corresponding to the tallest 5% of all men. Use a standard normal table or software to determine the z-score and calculate the height that corresponds to the result in part d (i)