What two scores would divide a normal distribution such that 64.26% of the general population falls within them if the mean is 100 and the standard deviation is 15?
A)80 to 120
B)85 to 115
C)90 to 110
D)75 to 125

Question

Quizplus · Accepted Answer

To find the scores that divide the normal distribution such that 64.26% of the population falls within them, we need to locate the z-scores that correspond to the 17.87th and 82.13th percentiles. Using a z-table or calculator, we can find that these z-scores are approximately -0.95 and 0.95, respectively.

To convert these z-scores to actual scores, we can use the formula: 
X = Z * SD + Mean

Plugging in the values, we get: 
Lower score: X = -0.95 * 15 + 100 = 85.75 
Upper score: X = 0.95 * 15 + 100 = 114.25

Therefore, the two scores that divide the normal distribution such that 64.26% of the population falls within them are 85 to 115, which corresponds to answer choice B.

What Two Scores Would Divide a Normal Distribution Such That