Question

# Below represent scores on an exam, each entry one score for one student 40 99 59...

Below represent scores on an exam, each entry one score for one student

 40 99 59 98 63 63 64 65 67 35 67 67 68 70 71 71 71 46 72 72 60 73 74 74 74 75 97 75 62 76 76 76 76 76 77 57 77 98 77 63 78 78 78 79 79 80 80 80 80 80 81 81 92 81 93 82 82 83 83 83 83 83 83 83 84 84 84 84 84 85 85 86 86 86 86 86 87 88 88 77 88 52 89 89 86 84 91 90 92 88 93 93 46 93 94 94 94 61 95 96 55 43 44 50 71 77 72 43 44
1. Estimate the number of students who would get points between 75 and 85 using normal distribution. Does it match with the actual data?

By calculation using excel formula average and stddev

mean = 76.6330

S.D. = 14.2111

P(75.0 < x < 85.0)=?

This implies that

P(75.0 < x < 85.0) = P(-0.1149 < z < 0.5888) = P(Z < 0.5888) - P(Z < -0.1149)

P(75.0 < x < 85.0) = 0.7220022770715641 - 0.45426219254773315

P(75.0 < x < 85.0) = {0.2677} . By calculation

n = 109

values between 75 to 85 = 38

P(75.0 < x < 85.0) = 0.2569 by actual data

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