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The Following Data Represent the Scores of a Sample of 50

question 51

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The following data represent the scores of a sample of 50 students on a statistics exam. The mean score is xˉ=80.3\bar { x } = 80.3 , and the standard deviation is s=11.37s = 11.37 .
4951596366686869707171717374767676777879797979808082838383858586868888888889898990919292939596979798\begin{array} { l l l l l l l l l l } 49 & 51 & 59 & 63 & 66 & 68 & 68 & 69 & 70 & 71 \\ 71 & 71 & 73 & 74 & 76 & 76 & 76 & 77 & 78 & 79 \\ 79 & 79 & 79 & 80 & 80 & 82 & 83 & 83 & 83 & 85 \\ 85 & 86 & 86 & 88 & 88 & 88 & 88 & 89 & 89 & 89 \\ 90 & 91 & 92 & 92 & 93 & 95 & 96 & 97 & 97 & 98 \end{array}
What percentage of the scores fall in each of the intervals xˉ±s,xˉ±2s\bar { x } \pm s , \bar { x } \pm 2 s , and xˉ±3s\bar { x } \pm 3 s ? Based on these percentages, do you believe that the distribution of scores is approximately normal? Explain.

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Definitions:

Status

A social or professional position, standing, or rank of an individual or group within a society or organization.

Status Inconsistency

Occurs when an individual occupies several differently ranked statuses at the same time.

Class Inconsistency

A situation where an individual's socioeconomic status in different dimensions of social class (like occupation, education, and income) do not align, leading to contradictions in class identity.

Dalai Lama

The title given to the spiritual leaders of the Tibetan people, recognized for their significant role in Buddhism and Tibetan politics.

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