If a distribution of scores is known to be normal and has a mean of 60 and a standard deviation of 7.33, what range of scores would include 99.74% of the scores?
A) 53-67
B) 45-75
C) 40-80
D) 38-82

Question

Quizplus · Accepted Answer

To find the range of scores that includes 99.74% of the scores, we need to find the z-scores that correspond to the 0.13% of scores on each tail (since 100% - 99.74% = 0.13% on each tail). Using a standard normal distribution table or calculator, we can find that the z-score for 0.13% is approximately ±2.64.

So, the range of scores that includes 99.74% of scores is from 
mean - 2.64(standard deviation) to mean + 2.64(standard deviation).
Substituting the values given in the question, we get:
60 - 2.64(7.33) to 60 + 2.64(7.33)
= 38.5 to 81.5

Therefore, the answer is D (38-82) as it is the only option that includes the range from 38.5 to 81.5.

If a Distribution of Scores Is Known to Be Normal