Question

Assume that adults have IQ scores that are normally distributed with a mean of mu equals 105?=105 and a standard deviation sigma equals 20?=20. Find the probability that a randomly selected adult has an IQ between 92 and 118.

Answer 1

Let the IQ score of the adult be denoted by the random variable X so X follows normal distribution with mean or ?=105 and ?=20 and the required problem requires us to calculate P( 92 < X < 118)

Now for X = Normal (?=105 , ?=20) , (X - 105)/ 20 let it be denoted by z will follow Standard Normal that is Normal (?= 0 , ?=1) .

So P( 92 < X < 118 ) = P((92 - 105)/ 20 < (X - 105)/ 20 < (118 - 105)/ 20)

= P( -13/20 < z < 13/20)

= P(z < 13/20) - P( z < -13/20)

( Now P(z < -13/20 ) = 1 - P( z < 13/20 ) so putting this equation in the previous one we get )

= 2 * P(z <13/20) - 1

= 0.4844

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