Suppose That a Random Sample of 150 Observations Was Drawn

Essay

Suppose that a random sample of 150 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 intervals below was counted. Can we infer at the 5% significance level that the data were drawn from a normal population?
$$\begin{array} { | l | c| } \hline \text { Intervals } & \text { Frequency } \\\hline Z \leq - 1.5 & 15 \\- 1.5 < Z \leq - .5 & 32 \\- .5 \leq Z \leq .5 & 65 \\.5 < Z \leq 1.5 & 25 \\Z > 1.5 & 13 \\\hline\end{array}$$