ACT scores have a mean of 214 and 10 percent of the scores a

ACT scores have a mean of 21.4 and 10 percent of the scores are above 27. The scores have a distribution that is approximately normal. Find the standard deviation. Round your answer to the nearest tenth, if necessary.

Solution

The z score corresponding to the top 10% of scores is

z = 1.281551566

Thus,

z = (x-u)/sigma

sigma = (x-u)/z = (27-21.4)/1.281551566

sigma = 4.369703216 [ANSWER]