Suppose that a random sample of 100 observations was drawn from a population. After calculating the mean and standard deviation, each observation was standardized and the number of observations in each of the following intervals was counted. Can we infer at the 5% significance level that the data were not drawn from a normal population?

Interval Frequency

Z ≤ 1.5 ...........10

−1.5 < Z ≤ −0.5 .......18

−0.5 < Z ≤ 0.5 .........48

0.5 < Z ≤ 1.5 ........16

Z > 1.5 .......... 8