The grade point averages of a large population of college students are approximately normally distributed with a mean of 2.4 and
a standard deviation of 0.8.What is the probability that a randomly selected student will have a grade point average in excess of 3.0? Round your answer to 4 decimal places.
We know that the grade point averages of a large population of college students are approximately normally distributed with a mean of 2.4 and a standard deviation of 0.8. The z-score related to 3.0 is computed as (3.0-2.4)/0.8 = 0.75. Therefore the probability that a randomly selected student will have a grade point average in excess of 3.0 is P(Z > 0.75) where Z comes from a standard normal distribution. So, P(Z > 0.75) = 0.2266
