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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?

Answer :

Answer:

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<x) = 1 - 0.15 = 0.85

Since P(z<x) = ¢(Z) = 0.85

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<x) = 0.35

Since P(z<x) = ¢(Z) = 0.35

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<z<y) = 0.8 = 0.9 - 0.1

Since P(z<x) = ¢(Z)

P(x<z<y) = 0.9 - 0.1 = ¢(Z1) - ¢(Z2)

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

24nthuynh

Answer:

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<x) = 1 - 0.15 = 0.85

Since P(z<x) = ¢(Z) = 0.85

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<x) = 0.35

Since P(z<x) = ¢(Z) = 0.35

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<z<y) = 0.8 = 0.9 - 0.1

Since P(z<x) = ¢(Z)

P(x<z<y) = 0.9 - 0.1 = ¢(Z1) - ¢(Z2)

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

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