Question

Use the Normal model ​N(101​,20​) for the IQs of sample participants. ​a) What IQ represents the 13th ​percentile? ​b) What IQ represents the 90th ​percentile? ​c) What's the IQR of the​ IQs? ​a) The IQ representing the 13th percentile is nothing.

Answer 1

Given that,

(a)

P(Z < -1.13) = 0.13

z = -1.13

Using z-score formula,

x = z * +

x = -1.13 * 20 + 101 = 78.4

13th percentile = 78.4

(b)

P(Z < 1.28) = 0.90

z = 1.28

Using z-score formula,

x = z * +

x = 1.28 * 20 + 101 = 126.6

90th percentile = 126.6

(c)

Q1 = -0.67 * 20 + 101 = 87.6

Q3 =  0.67 * 20 + 101 = 114.4

IQR = Q3 - Q1 = 114.4 - 87.6 = 26.8