Question

Based on the normal model N (110,16) describing IQ scores, what would the z scores be for people with the following IQs:

a) 80

b) 90

c) 112 and 132

Thank you.

Answer 1

a)

Here, μ = 110, σ = 16 and x = 80. We need to compute P(X <= 80). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (80 - 110)/16 = -1.88

b)

Here, μ = 110, σ = 16 and x = 90. We need to compute P(X <= 90). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (90 - 110)/16 = -1.25

c)

Here, μ = 110, σ = 16, x1 = 112 and x2 = 132. We need to compute P(112<= X <= 132). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (112 - 110)/16 = 0.13
z2 = (132 - 110)/16 = 1.38