Suppose that the mean and standard deviation of the scores o

Suppose that the mean and standard deviation of the scores on the mathematics portion of the SAT are 494.87 and 66.717, respectively, for a given year. 14.68% of students scored greater than what score? Assume the distribution is approximately normal.

Solution

Mean = 494.87

and std dev = 66.717

Cumulative prob for X<x is 100-14.68% = 85.32%

Or Prob score for Z<z = 0.8532

z = 1.05

Hence X = 494.87+1.05(66.717)

=564.9229

Hence 14.68% students scored greater than 564.9229 scores.