What percentage of the population scored between 80 and 110 points on this exam ?

Question

Mean Score 100

Standard Deviation 16

Answer 1

x = score want to find probability x between 80 and 110: P(80 < x < 110)

z = (x - mean)/SD

mean = 100, SD = 16

translate P(80 < x < 110) to P(? < z < ?)

compute z score for x = 80: z = (80 - 100)/16 = -1.25

compute z score for x = 110: z = (110-100)/16 = 0.625

P(-1.25 < z < 0.625) = P(z < 0.625) - P(z < -1.25) = 0.734 - 0.1056 = 0.6284