Question

Use the Normal model ​N(105​,18​) for the IQs of sample participants. ​a) What IQ represents the 19th ​percentile? ​b) What IQ represents the 98th ​percentile? ​c) What's the IQR of the​ IQs?

Answer 1

Given that,

mean = = 105

standard deviation = = 18

(a)

P(Z < -0.88) = 0.19

z = -0.88

Using z-score formula,

x = z * +

x = -0.88 * 18 + 105 = 89.16

19th percentile = 89.16

(b)

P(Z < 2.05) = 0.98

z = 2.05

Using z-score formula,

x = z * +

x = 2.05 * 18 + 105 = 141.9

98th percentile = 141.9

(c)

Q1 is,

P(Z < -0.67) = 0.75

z = -0.67

Using z-score formula,

x = z * +

x = -0.67 * 18 + 105 = 92.94

Q1 = 92.94

Q3 is,

P(Z < 0.67) = 0.25

z = 0.67

Using z-score formula,

x = z * +

x = 0.67 * 18 + 105 = 117.06

Q3 = 117.06

IQR = Q3 - Q1 = 117.06 - 92.94 = 24.12