Question 1: A long-term record for weather in a certain province shows that the annual precipitation has a mean of 39.67 inches and a standard deviation of 4.38 inches. If the annual precipitation amount has a normal distribution, what is the probability that next year the total precipitation will be:
a. more than 50.0 inches?
b. between 42.0 and 48.0 inches?
c. between 30.0 and 37.5 inches?
d. more than 35.0 inches?
e. less than 45.0 inches?
f. less than 32.0 inches?
Problem 2: Consider that the age (x) of urban youth in Toronto is distributed normally, with µ = 24.7 and σ = 4.5.
a. Calculate the z-score for an age of 21.5.
b. Calculate the z-score for an x¯ of 21.5 from a sample of size 25.
c. Explain how 21.5 can have such different z-scores.