Question

Use the Normal model ​N(100​,15) for the IQs of sample participants.

​a) What IQ represents the 20th ​percentile?

​b) What IQ represents the 99th ​percentile?

​c) What's the IQR of the​ IQs?

Answer 1

Given that,

mean = = 100

standard deviation = = 15

(a)

P(Z < -0.84) = 0.20

z = -0.84

Using z-score formula,

x = z * +

x = -0.84 * 15 + 100 = 87.4

20th percentile = 87.4

(b)

P(Z < 2.326) = 0.99

z = 2.326

Using z-score formula,

x = z * +

x = 2.326 * 15 + 100 = 134.89

99th percentile = 134.89

(c)

(b)

P(Z < -0.67) = 0.25

z = -0.67

Using z-score formula,

x = z * +

x = -0.67 * 15 + 100 = 89.85

Q1 = 89.95

P(Z < 0.67) = 0.25

z = 0.67

Using z-score formula,

x = z * +

x = 0.67 * 15 + 100 = 110.05

IQR = Q3 - Q1 = 110.05 - 89.85 = 20.2