Question

Grades on a biology exam are approximately normally distributed with a mean of 78 and a standard deviation of 8. Originally Dr. Smith decides to curve course grades as follows: Students who score above the 90 percentile will receive an A Students whose scores are in the 80-89.percentiles receive a B Students whose scores are in the 70th-795h percentiles receive a C Students whose scores are in the 60-69 percentiles receive a D Students who score below the 60th percentile receive an F Find the Z-scores corresponding to the following percentiles (show work):

Answer 1

Given that Mean (u) 78 Standard deviation (o ) = 8 The student who score above the 90 Percentile W il receive an A U sing Ex cel function =NORM IN V (0.90, 78,8) 88.25 88 0.05 90% 0.04 0.03 0.02 0.01 0.00 50 60 70 Mean =78 80 90 x 88 100 The student who score are in 80 -89 th Percentile recieve B The student who score are in 80Percentile U sing Excel function =NORM IN v (0.80,78,8) 84.73 85 The student who score are in 89 Percentile U sing Excel function =NORM IN v (0.89,78,8) =8 7.81 88 0.05 0.04 B (80-89th percentile 0.03 0.02 0.01 0.00 50 70Mean 78 80 85 88 90 60 100 Density Density

The student who score are in 70 -79 th Percentile recieve C The student who score are in 70 Percentile U sing Excel function NORM IN V (0.70,78,8) 82.19 82 The student who score are in 79" Percentile U sing Excel function =NORM IN V (0.79,78,8) =84.45 84 0.05 C(70-79th Percentile 0.04 0.03 0.02 0.01 0.00 50 70Mean 78 80 82 84 60 90 100 The student who score are in 60 -69 th Percentile recieveD The student who score are in 60Percentile U sing Excel function =NORM IN V (0.60,78,8) -80.026 80 The student who score are in 69" Percentile U sing Excel function =NORM IN V (0.69,78,8) -8 1.97 82 0.05 D(60-69th Percentile 0.04 0.03 0.02 0.01 0.00 70Mean 78 80 82 60 90 100 Density Density

The student who score below 60 Percentile recieve E U sing Ex cel function =NORM IN V (0.60.78,8) - 80.026 80 0.05 E (Below 60th Percentile) 0.04 0.03 0.02 0.01 0.00 50 70Mean 78 80 60 90 100 Z - score corre sponding to 90"" Percentiles U sing Excel function =NORM S IN V (0.90,78,8) =1.28 Z - score corre sponding to the 80 Percentiles U sing Excel function =NORM SIN V (0.80) 0.84 Z - score corre sponding to the 70"% Percentiles U sing Excel function =NORM SINV (0.70) =0.52 Z - score corre sponding to the 60" Percentiles U sing Excel function =NORM SIN V (0.60) =0.25 Density

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