Refer to the scores of Mr. Pryor\'s statistics students on their first test. (me

Question

Refer to the scores of Mr. Pryor's statistics students on their first test. (mean: 80 standard deviation: 6.07)

(a) Mr. Pryor decides that the test scores are a little low. One option he considers is adding 4 points to each student's score. How will this affect each student's z-score? Their percentile?

(b) Rather than adding 4 points, Mr, Pryor also thinks about multiplying each student's score by 1.06. How will this affect each student's z-score? Their percentile?

(c) The last idea Mr. Pryor contemplates is determining each student's final score as follows: 84 + (student's z score)(4 points). Which of the tree plans --a, b, or c- would you recommend? Explain your reasoning.

Explanation / Answer

Mean score = 80

Standard deviation = 6.07

(a) Added 4 points to each student's score.

But it will not effect their Z - score as Z score is dependent only on the difference of mean and the value of the sample so it will not affect the Z - score. Similarly, it will not affect the percentile too.

(b) If we multiply each score by 1.06 then both mean and the value of the point will also be increased by 1.06. SImilarly, it will also increase the value of standard deviation by 1.06

Z = (Mean - Sample point)/ standard deviation

so, Z - score will not get affected so there is no change.

(c) Final Score = 84 + student's Z score = 84 + (Mean value - Score of student)/ Standard deviation

Final Score = 84 + (80 - previous score)/ 6.07

so here we will device the plan that we will use the c value because it will increase the test scores of students.

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