Use the data from University A in Table 7.

(a) Determine the minimum percentage of students who have IQ scores within 3 standard deviations of the mean according to Chebyshev’s Inequality.

(b) Determine the minimum percentage of students who have IQ scores between 67.8 and 132.2, according to Chebyshev’s Inequality.

(c) Determine the actual percentage of students who have IQ scores between 67.8 and 132.2.

Approach

(a) Use Chebyshev’s Inequality with k = 3.

(b) Determine the number of standard deviations 67.8 and 132.2 are from the mean of 100.0. Then substitute this value for k into Chebyshev’s Inequality.

(c) Refer to Table 7 and count the number of observations between 67.8 and 132.2. Divide this result by 100, the number of observations in the data set.

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Table 7 University A University B 73 103 91 93 136 108 92 104 90 78 86 91 107 94 105 107 89 96 102 96 108 93 91 78 81 130 82 86 111 93 92 109 103 106 98 95 97 95 109 109 102 111 125 107 80 90 122 101 82 115 93 91 92 91 117 108 89 95 103 109 103 110 84 115 85 83 131 90 90 103 106 110 88 97 119 90 90 99 96 104 98 95 71 69 97 130 91 62 85 94 110 85 87 105 111 87 103 92 103 107 106 97 102 109 105 97 104 94 92 107 94 112 113 115 106 97 106 888 83 94 114 107 108 89 96 107 107 96 95 117 97 85 99 98 89 104 99 99 87 91 105 109 108 102 109 76 94 103 112 107 101 91 107 116 107 90 98 98 92 119 96 118 98 107 110 106 103 93 110 125 101 91 119 97 106 114 87 107 96 93 99 89 94 118 85 127 141 129 60 115 80 111 79 104 88 99 97 106 107 112 97 94 107