Some IQ tests are standardized to a Normal model N (100 ,18 ). a) What cutoff value bounds the highest 15 % of all IQs? b) What cutoff value bounds the lowest 35 % of the IQs? c) What cutoff values bound the middle 80 % of the IQs?

Question

Mathematics

Declan Morrison

4 May, 01:24

Some IQ tests are standardized to a Normal model N (100 ,18 ). a) What cutoff value bounds the highest 15 % of all IQs? b) What cutoff value bounds the lowest 35 % of the IQs? c) What cutoff values bound the middle 80 % of the IQs?

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Answers (1)

Know the Answer?

Lyla Doyle · Answer 1

A) 119

B) 93

C) 77 and 123

Step-by-step explanation:

Mean m = 100

Standard deviation d = 18

A) IQ value for the highest 15% of the IQ;

P (z
Since P (z
Z = 1.04

Recall that,

Z = (x-m) / d

x = dZ + m = 1.04*18 + 100

x = 118.72 approximately

x = 119

Therefore, the cutoff value bounds the highest 15 % of all IQs is 119

B) For the lowest 35 % of the IQs

P (z
Since P (z
Z = - 0.39

Recall that,

Z = (x-m) / d

x = dZ + m = - 0.39*18 + 100

x = 92.98 = 93

Therefore, the cutoff value bounds the lowest 35 % of the IQs is 93

C) cutoff values bound the middle 80 % of the IQs

P (x
Since P (z
P (x
Z1 = 1.28

Z2 = - 1.28

Recall that,

Z1 = (x-m) / d

x = dZ1 + m = 1.28*18 + 100

x = 123

Z2 = (y-m) / d

y = dZ2 + m = - 1.28*18 + 100

y = 77

Therefore, cutoff values bound the middle 80 % of the IQs are 77 and 123