22 12 Quest Score: 0 of 1 pt Consider the sample of exam scores to the right, ar

Question

22 12 Quest Score: 0 of 1 pt Consider the sample of exam scores to the right, arranged in increasing order. The sample mean and sample standard deviation of these exam scores are, respectively, 83.4 and 16.5. Chebychevs rule states that for any data set and any real number k > 1, at least 100 (1-1/k) % of the observations lie within k standard deviations to either side of the mean. Complete parts (a) and (b) below 26 54 55 61 65 72 76 81 81 81 85 89 90 90 90 90 90 90 91 92 92 92 94 94 95 95 95 97 98 100 a. Use Chebychev's rule to obtain a lower bound on the percentage of observations that lie within three standard deviations to either side of the mean. 889%(Round to one decimal place as needed.) b. Use the data to obtain the exact percentage of observations that lie within three standard deviations to either side of the mean Round to one decimal place as needed.)

Explanation / Answer

b. At standard deviation of 3, the upper and lower range of the dataset will be 83.4+3 =86.4 & 83.4-3=80.4.

Now observe count thetnumbers in dataset thattlie within this range.

Clearly, there are 4 values out of 30.

=4/30%

=13.33%

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