Question

Statistics exam scores follow a standard normal distribution with mean 0 and standard deviation 1. Find each of the following probabilities of the given scores.

(a)Less than 2.71

(b)Greater than -0.96

(c)Less than -2.18

(c)Between -1.30 and 0.45

(d)Find the 75th percentile of these Statistics exam scores.

(e) Find the Statistics exam scores that can be used as cutoff values separating the most extreme (high and low) 2% of all scores.

Answer 1

The values corresponding to the given scores shall be obtained from the standard normal distribution table.

a) P(less than 2.71) = P(Z < 2.71)

= 0.9966

b) P(greater than -0.96) = P(Z > -0.96)

= 1 - P(Z < -0.96)

= 1 - 0.1685

= 0.8315

c) P(less than -2.18) = P(Z < -2.18)

= 0.0146

d) Let S be the 75th percentile

P(Z < S) = 0.75

Take Z score closes to 0.7500 from standard normal distribution table.

S = 0.67

75th percentile = 0.67

e) Let the cutoff be between L and H

P(X < L) = 0.02/2 = 0.01

L = -2.33

P(X < H) = 0.99

H = 2.33

Cutoff values separating the most extreme (high and low) 2% of all scores = -2.33 and 2.33