Suppose that grade point averages of undergraduate students

Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.54 and a standard deviation of 0.44. Using the empirical rule, what percentage of the students have grade point averages that are at least 2.1? Please do not round your answer

Solution

Let X be a random variable denoting the grade point average of a undergraduate student at one university.

X~N(2.54,0.44²) since only normal distribution is bell shaped.

The probability that a student have grade point average is atleast 2.1=P(X>=2.1)=1-P(X<2.1)=1-0.158655=0.841345