Question 9 of 11 , Step 1 of 1 $9 / 15$ Correct 0 Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.55 and a standard deviation of 0.45 . Using the empirical rule, what percentage of the students have grade point averages that are between 1.65 and 3.45 ? Answer How to enter your answer (opens in new window) Tables Keypad Keyboard Shortcuts $\%$

Step 1 ：The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution, almost all data falls within three standard deviations of the mean. Specifically, 68% of data falls within one standard deviation, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

Step 2 ：In this case, the mean is 2.55 and the standard deviation is 0.45. The range 1.65 to 3.45 is exactly two standard deviations away from the mean (2.55 - 0.45*2 = 1.65 and 2.55 + 0.45*2 = 3.45).

Step 3 ：Therefore, according to the empirical rule, approximately 95% of students have grade point averages that fall within this range.

Step 4 ：The percentage of the students that have grade point averages between 1.65 and 3.45 is approximately \(\boxed{95\%}\).