Question

Percentage grades in a large geography class follow a normal distribution with mean 67.5 and standard deviation 12.5.

What proportion of students in the class receive percentage grades between 60 and 70?
(A) 0.2650 (B) 0.2750 (C) 0.2850 (D) 0.2950 (E) 0.3050

Answer 1

To find the proportion of students in the class who receive percentage grades between 60 and 70, we can use z-scores and a standard normal distribution table. The proportion is estimated to be e. 0.3050.

Step-by-step explanation:

To find the proportion of students in the class who receive percentage grades between 60 and 70, we need to find the area under the normal distribution curve between those two values. First, we need to calculate the z-scores for both grades:

For grade 60:
z = (60 - 67.5) / 12.5 = -0.6

For grade 70:
z = (70 - 67.5) / 12.5 = 0.2

Next, we can use a standard normal distribution table to find the proportions: The area to the left of a z-score of -0.6 is 0.2743, and the area to the left of a z-score of 0.2 is 0.5793.

Therefore, the proportion of students in the class who receive percentage grades between 60 and 70 is:

0.5793 - 0.2743 = e. 0.3050