Assume that a set of test scores is normally distributed with a mean of 100 and

Question

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.

Explanation / Answer

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%

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