Please show all work. Thank you! Total scores. Here are the total scores of 10 s

Question

Please show all work. Thank you! Total scores. Here are the total scores of 10 students 62 93 54 76 73 98 64 55 80 71 hould come from a distribution that is approxi- 1.120 in an introductory statistics course: ,ISTAT Previous experience with this course suggests t hat these mat ely Normal with mean 72 and standard deviation 10. (a) Using these values for and , standardize the scores of these 10 students. (b) If the grading policy is to give a grade of A to the top 15% of scores based on the Normal distribution with mean 72 and standard deviation 10, what is the cutoff for an A in terms of a standardized score? (c) Which of the 10 students earned a grade of A in the course? Show your work.

Explanation / Answer

a) For Standardized scores

Use formula

z = (Score-72)/10

For score 62

z = (62-72)/10 = -1

Similarly z score

62 -1

93 2.1

54 -1.8

76 0.40

73 0.10

98 2.6

64 -0.8

55 -1.7

80 0.8

71 -0.10

b) Critical value for top 15% is 1.0364

Cutoff Score = 1.0364*72+10 = 84.62

c) All scores greater than 10 earned grade A

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