5.36 Scores on an achievement test are known to be normally distributed with a mean of 420 and a standard deviation of 80.

a. For a randomly chosen person taking this test, what is the probability of a score between 400 and 480?

b. What is the minimum test score needed in order to be in the top 10% of all people taking the test?

c. For a randomly chosen individual, state, without doing the calculations, in which of the following ranges his score is most likely to be: 400–439, 440–479, 480–519, or 520–559.

d. In which of the ranges listed in part

(c) is the individual’s score least likely to be?

e. Two people taking the test are chosen at random.

What is the probability that at least one of them scores more than 500 points?