1.) Standing eye heights of women are normally distributed with a mean of 1516 mm and a standard deviation of 63 mm (based on anthropometric survey data from Gordon, Churchill, et al.). a.) A door...

1.) Standing eye heights of women are normally distributed with a mean of 1516 mm and a standard
deviation of 63 mm (based on anthropometric survey data from Gordon, Churchill, et al.).
a.) A door peephole is placed at a height that is uncomfortable for women with standing eye heights
greater than 1605 mm. What percentage of women will find that height uncomfortable?
b.) In selecting the height of a new door peephole, the architect wants its height to be suitable for the
highest 99% of standing eye heights for women. What standing eye height of women separates the
highest 99% from the lowest 1%?
c.) What percentage of women have a standing eye height between 1420 mm and 1560 mm?
d.) What is the probability that a group of twenty women have an average standing eye height that is
less than 1500 mm? Even though our sample size is less than thirty, why can the Central Limit Theorem
still apply here?