Question

The scores on a statistics test are Normally distributed with parameters µ = 75 and σ = 10.

Find the probability that a randomly chosen score is

(a) no greater than 60

(b) at least 90

(c) between 60 and 90

(d) between 65 and 85

(e) at least 75

Answer 1

z = (x - μ)/ σ

a) no greater than 60

z = (60-75)/10 = -1.5

P(z < -1.5) = 0.9332

=1-0.9332 = 0.0668

(b) at least 90

z = (90-75)/10 = 1.5

P(Z < 1.5) = 0.9332

(c) between 60 and 90

z = (60-75)/10 = -1.5

z = (90-75)/10 = 1.5

P(-1.5 < z < 1.5) = 0.8664

(d) between 65 and 85

z = (65-75)/10 = -1.0

z = (85-75)/10 = 1.0

P(-1.0 < z < 1.0) = 0.6827

(e) at least 75

z = (75-75)/10 =0

P(Z < 0) = 0.5