Question

Assume that adults have IQ scores that are normally distributed with a mean of μ= 105 and a standard deviation Ï =20 . Find the probability that a randomly selected adult has an IQ between 85 and 125 .

Answer 1

0.68268

Explanation:

We solve using z score

z = (x-μ)/σ, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

For x = 85

z = 85 - 105/20

z = -1

Probability value from Z-Table:

P(x = 85) = 0.15866

For x = 125

z = 125 - 105/20

z = 1

Probabilty value from Z-Table:

P(x = 125) = 0.84134

The probability that a randomly selected adult has an IQ between 85 and 125 is calculated as:

P(x = 125) - P(x = 85)

= 0.84134 - 0.15866

= 0.68268