Question

Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 13. Use the empirical rule to determine the following. ​

(a) What percentage of people has an IQ score between 61 and 139?

​(b) What percentage of people has an IQ score less than 74 or greater than 126? ​

(c) What percentage of people has an IQ score greater than 113? ​

Answer 1

This is a normal distribution question with

Type of this part: 3

a) x1 = 61

x2 = 139

P(61.0 < x < 139.0)=?

This implies that

P(61.0 < x < 139.0) = P(-3.0 < z < 3.0) = P(Z < 3.0) - P(Z < -3.0)

P(61.0 < x < 139.0) = 0.9986 - 0.0013499

P(61.0 < x < 139.0) = {0.9973}

b) x1 = 74

x2 = 126

P(X < 74.0 or X > 126.0)=?

This implies that

P(X < 74.0 or X > 126.0) = P(z < -2.0 or z > 2.0) = 0.0455

c) x = 113

P(x > 113.0)=?

The z-score at x = 113.0 is,

z = {113.0-100.0}/{13.0}

z = 1.0

This implies that

P(x > 113.0) = P(z > 1.0) = 1 - 0.84134

P(x > 113.0) = {0.1587}

PS: you have to refer z score table to find the final probabilities.

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