Question

A students received a score of 50 on his history test. The test had a mean of 69 and a standard deviation of 10. Find the z score and assess whether his score is considered unusual.

Answer 1

`z = (x - mean)/(stdev) \\ \\ z = (50 - 69)/(10) = -1.9`

The general rule is that 68% of all scores are within 1 z-score of the mean.
95% are within 2 z-scores of the mean.
99% are within 3 z-scores of the mean.

1.9 is pretty close to 2, so this means approximately only 5% of all scores are more unusual than this students' score.