Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard deviation σ=15. Find the probability that a randomly selected adult has an IQ between 90 and 120.

Question

Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard deviation σ=15. Find the probability that a randomly selected adult has an IQ between 90 and 120.

The probability that a randomly selected adult has an IQ between

90 and 120 is __.

Answer 1

if x is IQ want to find

P(90 < x < 120)

transform inequality to standard normal (z), where z = (x - mean)/SD = (x -105)/15:

P( (90-105)/15 < z < (120-105)/15)

= P( -1 < z < 1)

= P(z < 1) - P(z < -1) = 0.8413 - 0.1587 = 0.6826