Heights of 10 year old children, regardless of sex, closely follow a normal distribution with mean 55.3 inches and standard deviation 5.9 inches.Round answers to 4 decimal places.

a) What is the probability that a randomly chosen 10 year old child is less than 47.7 inches?

b) What is the probability that a randomly chosen 10 year old child is more than 58.8 inches?

c) What proportion of 10 year old children are between 52.9 and 58.8 inches tall?

d) 90% of all 10 year old child are less than inches.