(2 points) Final exam scores in a mathematics course are normally distributed wi

Question

(2 points) Final exam scores in a mathematics course are normally distributed with a mean of 80 and a standard deviation of 12. Based on the above information and a Z-table, fill in the blanks in the table below. Precision and other notes: (1) Percentiles should be recorded in percentage form to three decimal places. (2) Note that this problem does not use the rough values of the 68-95-99.7 rule (that is, the empirical rule); instead you must use more precise Z-table values for percentiles. Please calculate z-scores to 2 decimal places Exam score Z-score Percentile 116 71.96 74.86

Explanation / Answer

Here there are four parts of the question

Par(a) Exam score X = 116

Z = (116 - 80)/12 = 3

Percentile = Pr( Z < 3) = 99.865%

Part(b)

Z = (71.96 - 80)/12 = -0.67

Percentile = Pr(Z < -0.67) = 25.143%

Part (c)

Z - score = 1

X = 80 + 1 * 12 = 92

Percentile = Pr(Z < 1) = 84.134%

Part(d)

Percentile = 74.86

so Z = 0.67

Exam score = 80 + 0.67 * 12 = 88.04

The completed table is given below.

Here note : I have calculated all values from standard Z table

EXAM SCORE Z score Percentile 116 3 99.865 71.96 -0.67 25.143 92 1 84.134 88.04 0.67 74.86

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