1) Count the number of sample means in Table 7.1 that are larger than 104.0. Use this count to obtain the probability that in the simple random sampling of two taxpayers from eight that the sample mean actually obtained will overestimate the true mean by at least 12.5.

2) Count the number of sample means in Table 7.1 that are smaller than 78.0. Use this count to obtain the probability that the sample mean actually obtained will underestimate the true mean by at least 13.5.

3) Use the results of Exercises 1 and 2 to find the probability that the particular sample mean obtained by simple random sampling will either be an overestimate of at least 12.5 or an underestimate of at least 13.5.

Here is the table used for the questions

TABLE 7.1 EXACT CONFIDENCE INTERVALS OF SIZE 24/28 FOR THE MEAN OF THE TAXPAYER POPULATION (2 taxpayers from 8) Covers Sample Mean Lower Limit Upper Limit True Mean? 64.0 40.5 88.5 no 66.0 42.5 90.5 no 70.0 46.5 94.5 yes 75.0 51.5 99.5 yes 77.0 53.5 101.5 yes 79.0 55.5 103.5 yes 81.0 57.5 105.5 yes 81.0 57.5 105.5 yes 83.0 59.5 107.5 yes 85.0 61.5 109.5 yes 87.0 63.5 111.5 yes 88.0 64.5 112.5 yes 92.0 68.5 116.5 yes 92.0 68.5 116.5 yes 94.0 70.5 118.5 yes 95.0 71.5 119.5 yes 96.0 72.5 120.5 yes 98.0 74.5 122.5 yes 99.0 76.5 123.5 101.0 yes 77.5 125.5 103.0 yes 79.5 127.5 105.0 yes $81.5 109.0 129.5 yes 85.5 110.0 133.5 86.5 yes 112.0 134.5 88.5 yes 116.0 136.5 92.5 yes 123.0 140.5 99.5 no 145.5 no