3.17 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.

Percentages are close to 68-95-99.7%, we can declare that yes, the 68-95-99.7% rule is roughly followed and yes data appear to follow a normal distribution.

What is a normal distribution?

It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

We have a data of final exam scores of 20 Introductory.

a) Range of 1 standard deviation:

(77.7 – 8.44, 77.7 + 8.44) [69.3, 86.1]

Range of 2 standard deviation:

(77.7 – 2(8.44), 77.7 + 2(8.44)) [60.8, 94.6]

Range of 3 standard deviation:

(77.7 – 3(8.44), 77.7 + 3(8.44)) [52.4, 103.0]

Number of data points lie within 1 standard deviation = 14

Percent of data points lie within 1 SD = (14/20)×100 = 70%

Number of data points lie within 2 SD = 19

Percent of data points lie within 1 SD = (19/20)×100 = 95%

Number of data points lie within 3 SD = 20

Percent of data points lie within 1 SD = (20/20)×100 = 100%

Because these percentages are close to 68-95-99.7%, we can declare that yes, the 68-95-99.7% rule is roughly followed.

b)

Because the histogram in the graph is symmetric, and the normal probability plot reveals that the points are very close to a straight line, the data appears to follow a normal distribution.

Thus, percentages are close to 68-95-99.7%, we can declare that yes, the 68-95-99.7% rule is roughly followed and yes data appear to follow a normal distribution.

Learn more about the normal distribution here:

brainly.com/question/12421652

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