Question

4.127 Rankings of research universities. Refer to the CollegeChoice2015 Rankings of National Research Universities,Exercise 2.110 (p. 125). Data on academic reputation scores for the top 50 research universities (saved in the file) are listed in the accompanying table. Would you recommend using the normal distribution to approximate the distribution of academic reputation scores?

99 92 94 95 97 91 91 92 92 89 84 85 100 87 83

83 89 79 94 79 79 87 76 67 76 76 76 70 74 64

74 69 66 72 65 76 64 65 61 69 62 69 52 64 64

47 60 57 63 62

Short answer

The quantile- quantile line and data points are not falling approximately one upon another. So, the normally distributed data score is not recommended.

Step-by-step solution

Given information

Data on academic reputation scores for the top 50 research universities are listed in the accompanying table.

Plotting the graph

The above graph shows that the data points do not fall in a straight line.

The maximum data points fall below the quantile-quantile line. The lower portions of the data points above the line and upper portion fall below the line, and only the middle portion of the data points fall on the line.

So, it can be said that the productivity score is not normally distributed, andthe normally distributed data score is entirely not recommended in this case.