The distribution of grades in an introductory finance class

The distribution of grades in an introductory finance class is normally distributed, with an expected grade of 69. If the standard deviation of grades is 6, in what range would you expect 68 percent of the grades to fall? (Round answer to 2 decimal places, e.g. 15.25.)

Solution

This question is based on 68-95-99 rule, according to which in a normal distribution,

68% of observations lie within +/-1 standard deviation of expected number

95% of observations lie within +/-2 standard deviation of expected number

99% of observations lie within +/-3 standard deviation of expected number

So, for this question, we need to calculate 68% of observations --> +/-1 standard deviations

Range would be: (69 - 6) till (69 + 6) = 63 till 75