3.6.2 Evaluating the normal approximation 3.17 Scores on stats final. Below are

Question

3.6.2 Evaluating the normal approximation 3.17 Scores on stats final. Below are final exam scores of 20 Introductory Statistics students. 57,66, 69, 71, 72, 73, 74, 77, 78, 78, 79, 79, 81, 81, 82, 83, 83, 88, 89, 94 (a) The mean score is 77.7 points. with a standard deviation of 8.44 points. Use this information (b) Do these data appear to follow a normal distribution? Explain your reasoning using the graphs 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 to determine if the scores approximately follow the 68-95-99.7% Rule. provided below. 90- 80 70 60 60 70 80 90 -2 Scores Theoretical Quantiles

Explanation / Answer

(a)

Percentage of observations that fall within one standard deviation of mean: 68.27 %

Percentage of observations that fall within two standard deviations of mean: 95.45 %

Percentage of observations that fall within three standard deviations of mean: 99.73 %

As above numbers prove that scores approximately follow the 68-95-99.7% Rule.

(b)

Provided histogram is symmetrical and unimodal. Curve drawn on the histogram appears to fit the distribution. Also scores on normal distribution plot are line hugging with an exception of outliers on tail ends.

Overall scores appear to be normally distributed.

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