Question

Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard deviation equals σ=20. Find the probability that a randomly selected adult has an IQ less than 137.

Answer 1

Probability that a randomly selected adult has an IQ less than 137 is 0.9452

Explanation:

Step 1:

Sketch the curve.

The probability that X<137 is equal to the blue area under the curve.

Step 2:

Since μ=105 and σ=20 we have:

P ( X<137 )=P ( X−μ<137−105 )= P(X−μ/ σ< 137−105/20 )

Since x−μ/σ=Z and 137−105/20=1.6 we have:

P (X<137)=P (Z<1.6)

Step 3:

Use the standard normal table to conclude that:

P (Z<1.6)=0.9452

∴ probability that a randomly selected adult has an IQ less than 137 is 0.9452.