The heights of children two years old are normally distributed with a mean of 80cm and a standard deviation of 3.6cm. Pediatricians regularly measure the heights of toddlers to determine whether there is a problem. There may be a problem when a child is in the top or bottom 5% of heights.
a. Determine the heights of two-year old children that could be a problem.
b. Fund the probability of these events
i. A two-year old child is taller than 90 cm
ii. A two-year old child is shorter than 85 cm
iii. A two-year old child is between 75 and 85 cm