Monkeys male heights are upon average 75 inches with standard deviation of 5 inches. Monkey females heights are upon average a bit shorter and less variable, with mean height of 70 inches and standard deviation of 4.5 inches. Assume both monkey male and female heights are normally distributed, and are independent. Male and Female monkey population is evenly distributed.
What is P(female monkeys >= 75 inches)?
What is the distribution of the heights of the monkey population?
What is the probability a monkey of the average female height is taller than a monkey randomly drawn from the monkey population?
What is the probability a monkey of the average male height is shorter than a monkey randomly drawn from the monkey population?