mean: 21.1 and the standard deviation 5.0. Are any of these values unusual? Why or why not?

Question

The ACT is an exam used by colleges and universities to evaluate undergraduate applicants. The test scores are normally distributed. In a recent year, the mean test score was 21.1 and the standard deviation was 5.0. The test scores of four students selected at random are 15, 22, 9, and 35. Are any of these values unusual? Why or why not?

Answer 1

This is not my subject, but, if one SD = 5, then 95% of scores will fall between two SD on each side.  So, 21.1 + 10 = 31.1, and 21.1 - 10 = 11.1.  So in a sample of 4, you have 50% falling outside of two std deviations, whereas you'd only expect 5% of samples to do so.  Further, 97.7% of samples will fall within 3 SD on each side.  So, 21.1 + 15 = 36.10, and 21.1 - 15 = 6.1.  So both scores of 9 and 35 fall within 3 SD, but, they together comprise 50% or half of your sampled scores.  It seems unlikely, but you have a very small sample size for your set.