Question

Act scores have a mean of 21 and 6 percent of the scores are above 28. The scores have a distribution that is approximately normal. Find the standard deviation. Round your answer to the nearest tenth, if necessary.

Answer 1

The standard deviation is approximately 3.4

Step-by-step explanation:

To find the standard deviation, we need to calculate the z-score of the given percentile. Since 6 percent of the scores are above 28, the z-score can be found using the z-table or a calculator.

First, find the z-score that corresponds to 6 percent using the z-table or a calculator. The z-score is approximately -1.556. Next, use the formula z = (x - μ) / σ, where z is the z-score, x is the value above which the desired percentile lies, μ is the mean, and σ is the standard deviation.

Plugging in the values, we have -1.556 = (28 - 21) / σ. Solving for σ, we get the standard deviation as approximately 3.4.