Question

The scores on the verbal section of a certain graduate school entrance exam have a mean of 153 and a standard deviation of 8.7. Scores on the quantitative section of the exam have a mean of 154 and a standard deviation of 8.9. Assume the scores are normally distributed. Students intending to study engineering in graduate school have a mean score of 178 on the quantitative section and a mean score of 156 on the verbal section.

a. Find the percentile of 178 on the quantitative section.

b. Find the percentile of 156 on the verbal section. Click the icon to view the table of standard scores

c. The percentile of 163 on the quantitative section is approximately

-3.5   0.02
-3   0.13
-2.9   0.19
-2.8   0.26
-2.7   0.35
-2.6   0.47
-2.5   0.62
-2.4   0.82
-2.3   1.07
-2.2   1.39
-2.1   1.79
-2   2.28
-1.9   2.87
-1.8   3.59
-1.7   4.46
-1.6   5.48
-1.5   6.68
-1.4   8.08
-1.3   9.68
-1.2   11.51
-1.1   13.57
-1   15.87
-0.95   17.11
-0.9   18.41
-0.85   19.77
-0.8   21.19
-0.75   22.66
-0.7   24.2
-0.65   25.78
-0.6   27.43
-0.55   29.12
-0.5   30.85
-0.45   32.64
-0.4   34.46
-0.35   36.32
-0.3   38.21
-0.25   40.13
-0.2   42.07
-0.15   44.04
-0.1   46.02
-0.05   48.01
0   50
0.05   51.99
0.1   53.98
0.15   55.96
0.2   57.93
0.25   59.87
0.3   61.79
0.35   63.68
0.4   65.54
0.45   67.36
0.5   69.15
0.55   70.88
0.6   72.57
0.65   74.22
0.7   75.8
0.75   77.34
0.8   78.81
0.85   80.23
0.9   81.59
0.95   82.89
1   84.13
1.1   86.43
1.2   88.49
1.3   90.32
1.4   91.92
1.5   93.32
1.6   94.52
1.7   95.54
1.8   96.41
1.9   97.13
2   97.72
2.1   98.21
2.2   98.61
2.3   98.93
2.4   99.18
2.5   99.38
2.6   99.53
2.7   99.65
2.8   99.74
2.9   99.81
3   99.87
3.5   99.98

Answer 1