How do I solve this standard deviation problem?

Question

Assume that the mathematics scores on the SAT are normally distributed with a mean of 500 and a standard deviation of 100. What percent of students who took the test have a mathematics score between 550 and 650?

busterwasmycat · Answer

use a z-score table to define the percentages for each of the two absolute (real) scores, and subtract to get the difference. Z score is the number of SD above (or below) mean so 550 would have a z score of +0.5, and 650 would have a zscore of +1.5.  Those two z-scores correspond to a percentage of the population above the mean.  subtract to get the difference between the two (the part that lies between 550 and 650).

az_lender · Answer

Use normal distribution table to find
P (-1/2 < z < 1/2).
Answer = 38.2%

Captain Matticus, LandPiratesInc · Answer

(550 - 500) / 100 = 50/100 = 0.5
(650 - 500) / 100 = 150/100 = 1.5

http://www.z-table.com/

z = 0.5 =>> 0.6915
z = 1.5 =>> 0.9332

0.9332 - 0.6915 =>
0.2417 =>
24.17%

How do I solve this standard deviation problem?

3 Answers