Scores on stats final. Below are final exam scores of 20 Introductory Statistics

Question

Scores on stats final. Below are final exam scores of 20 Introductory Statistics students. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 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 to determine if the scores approximately follow the 68-95-99.7% Rule. (b) Do these data appear to follow a normal distribution? Explain your reasoning using the graphs provided below.

Explanation / Answer

a) Range of 1 standard deviation:

(77.7 - 8.44, 77.7 + 8.44) i.e. (69.3, 86.1)

Range of 2 standard deviation:

(77.7 - 2(8.44), 77.7 + 2(8.44)) i.e. (60.8, 94.6)

Range of 3 standard deviation:

(77.7 - 3(8.44), 77.7 + 3(8.44)) i.e. (52.4, 103.0)

Number of data points lie within 1 SD = 14

% of data points lie within 1 SD = 14 / 20 * 100 = 70%

Number of data points lie within 2 SD = 19

% of data points lie within 1 SD = 19 / 20 * 100 = 95%

Number of data points lie within 3 SD = 20

% of data points lie within 1 SD = 20 / 20 * 100 = 100%

Since this percentages are close to 68-95-99.7%, we can say that yes, scores approximately follow the 68-95-99.7 rule.

b) Yes, the data seems to follow a normal distribution because the histogram in graph a is symmetric and the normal probability plot shows that the points are very close to a straight line.

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