Question

The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule.

(a) What proportion of the students scored at least 21 points on this test, rounded to five decimal places?

(b) What is the 63 percentile of the distribution of test scores, rounded to three decimal places?

Answer 1

Solution : x :scores on a recent test closely

µ = mean = 22 points

σ = standard deviation = 2 points.

a)

z = (x-µ)/σ

P(at least 21 points) = P(x≥21)

= 1 - p(x<21)

= 1 - P(z < (21-22)/2

= 1 - P(z<-0.5)

= 1 - 0.30854 (Using Normal Table)

= 0.69146

Answer : 0.69146

b)

For 63th percentile z = 0.33

x = zσ + µ = 0.33*2+22 = 22.660

Answer : 22.660