The Following Data Represent the Scores of a Sample of 50

Essay

The following data represent the scores of a sample of 50 students on a statistics exam. The mean score is $\bar { x } = 80.3 \text {, and the standard deviation is } s = 11.37$

$\begin{array} { l l l l l l l l l l } 49 & 51 & 59 & 63 & 66 & 68 & 68 & 69 & 70 & 71 \\ 71 & 71 & 73 & 74 & 76 & 76 & 76 & 77 & 78 & 79 \\ 79 & 79 & 79 & 80 & 80 & 82 & 83 & 83 & 83 & 85 \\ 85 & 86 & 86 & 88 & 88 & 88 & 88 & 89 & 89 & 89 \\ 90 & 91 & 92 & 92 & 93 & 95 & 96 & 97 & 97 & 98 \end{array}$
What percentage of the scores fall in each of the intervals $\bar { x } \pm s , \bar { x } \pm 2 s$ , and $\bar { x } \pm 3 s$ ? Based on these percentages, do you believe that the distribution of scores is approximately normal? Explain.