Question

What IQ scores put a person in… (a) the top 1%? (b) the top 53% (c) the bottom 67%? (d) the bottom 34%? mean 100 and standard deviation of 16

Answer 1

Solution:-

Given that,

mean = = 100

standard deviation = = 16

a) Using standard normal table,

P(Z > z) = 1%

= 1 - P(Z < z) = 0.01

= P(Z < z) = 1 - 0.01

= P(Z < z ) = 0.99

= P(Z < 2.33 ) = 0.99

z = 2.33

Using z-score formula,

x = z * +

x = 2.33 * 16 + 100

x = 137.28

b) Using standard normal table,

P(Z > z) = 53%

= 1 - P(Z < z) = 0.53

= P(Z < z) = 1 - 0.53

= P(Z < z ) = 0.47

= P(Z < -0.08 ) = 0.47

z = -0.08

Using z-score formula,

x = z * +

x = -0.08 * 16 + 100

x = 98.72

c) Using standard normal table,

P(Z < z) = 67%

= P(Z < z ) = 0.67

= P(Z < 0.44 ) = 0.67

z = 0.44

Using z-score formula,

x = z * +

x = 0.44 * 16 + 100

x = 107.04

d) Using standard normal table,

P(Z < z) = 34%

= P(Z < z ) = 0.34

= P(Z < -0.41) = 0.34

z = -0.41

Using z-score formula,

x = z * +

x = -0.41 * 16 + 100

x = 93.44