Question

Help me please, algebra 1 question.

Answer 1

Scores on a statewide standardized test are normally distributed with a mean of 12.89 and a standard deviation of 1.95. Certificates are given to students whose scores are in the top 2% of those who took the test. This means that they scored better than 98% of the other test takers. Marcus received his score of 13.7 on the exam and is wondering why he didn’t receive a certificate. Show all work to determine whether Marcus’ score was high enough to earn a certificate. Write a letter to Marcus explaining whether or not he will be receiving a certificate. Include a brief summary of your statistical analysis in your letter.

Answer 2

Scores on a statewide standardized test are normally distributed with a mean of 12.89 and a standard deviation of 1.95. Certificates are given to students whose scores are in the top 2% of those who took the test. This means that they scored better than 98% of the other test takers. Marcus received his score of 13.7 on the exam
Z score = (score - mean)/standard deviation
Marcus Z score = (13.7 - 12.89)/1.95 = 0.4154
Z(0.4154) = Pr(0.1735) or 17.35% + 50% = 67.35%
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The "cut off" mark for a certificate
Pr (0.48) or 48% = Z (2.05)
2.05 = [cut off mark - 12.89]/1.95
3.9975+ 12.89 = 16.8875 = 16.9 rounded

Answer 3

I'm sorry. whats Pr? And where did you get .48 to find the cut off mark? @valeriemc

Answer 4

valeriemc has used probabilities to solve it. pr means probability
and because the chances are 50% (whether marcus would receive the certificate or not that why the chances of receiving a certificate would be 50%)

and we are finding whether he was in the 2% list or not that's why 2% was subtracted from 50% which gave us 48% which is 0.48.

hope my explanation clears your thoughts

Answer 5

I'm still really confused..can someone help clear things up?