Question

4)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.

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

(b) What is the 31 percentile of the distribution of test scores, rounded to three decimal places?

Answer 1

4)

Solution :

Given that ,

mean = = 22

standard deviation = = 2

(a)

P(x 21) = 1 - P(x 21)

= 1 - P((x - ) / (21 - 22) / 2)

= 1 -  P(z -0.5)  

= 1 - 0.3085

= 0.6915

P(x 21) = 0.69150

Proportion = 0.69150

(b)

P(Z < z) = 31%

P(Z < -0.4959) = 0.31

z = -0.4959

Using z-score formula,

x = z * +

x = -0.4959 * 2 + 22 = 21.008

31th percentile = 21.008