The scores on a test are normally distributed, with a mean of 82 and standard deviation of 5. What percent of scores are between 72 and 92? Explain your answer.

Answer 1

(92-82)/5 = 10/5 = 2

(82-72)/5 = 10/5 = 2

all scores between 72 and 92 are within 2 standard deviations from the mean

by the empirical rule, that's 95% of the scores

for a more precise percentage use z tables or an on line z calculator with z=2 it will give you about 95.45%. If you found a -2 z score, it corresponds to an area below the normal curve of 0.02275. But that's just one tail. double it to get 0.0455. Subtract that from 1, to get 0.9545 = 95.45%