Assume the heights of women in a population follow the normal distribution with mean 64.3 and standard deviation 2.6 in.

a. a woman is randomly selected from the population. calculate the probability that the height for the woman is:

i. between 60 and 66 inches tall.

ii. over 67 inches tall

b. how tall is a woman whose height is at the 90th percentile?

c. what is the median height of women?

d. a certain woman has a height that is 0.5 standard deviations above the mean. what proportion of women are taller than she?

e. what height separates the smallest 10% of heights from the largest 90%?

f. five women are chosen at random from this population. what is the probability exactly one of them is more than 67 inches tall?