A certain type of door has a height of 1.98 m.

a) What is the proportion of individuals who will not hit their head in a

population whose size is normally distributed with an average of 1.74

m and a standard deviation of 0.1 m?

b) On a sample of 15 individuals, what is the probability

i. that the average height is at least 1.70 m.

ii. that there are exactly 4 who are at most 1.65 m tall.