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.

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% 
 
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 

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