Assume that a set of test scores is normally distributed wit

Assume that a set of test scores is normally distributed with a mean of 100 and a standard deviation of 5. Use the 68-95-99.7 rule to find the following quantities:

1. The percentage of scores less than 100 is ____%

2. The percentage of scores greater than 105 is ____%

3. The percentage of scores between 90 and 105 is ____%

Round all answers to one decimal place as needed

Guidance in explaining the rule to determine answer is appreciated for future understanding and application. Thank you in advance.

Solution

Draw the normal curve ( Remember it is symmetrical around the mean)

Mean=100 std=5

100 in the middle of the axis
95 is 1 std to the left; 105 is 1 std to the right ---------- 68% between them
90 is 2 std to the left ; 110 is 2 std to the right ---------- 95% between them
85 is 3 std to the left ; 115 is 3 std to the right ---------- 99.7% between them

1. The percentage of scores less than 100 is 50%

2. The percentage of scores greater than 105 is

(Greater than 100) -(Between 100 to 105) = 50 - 34 % = 16%

3. The percentage of scores between 90 and 105 is

(Between 90 to 100) + (Between 100 to 105) = 95/2 +34 = 81.5%