Question

Assume that adults have iq scores that are normally distributed with a mean of μ=100 and a standard deviation σ=15. find the probability that a randomly selected adult has an iq less than 130

Answer 1

The probability that a randomly selected adult has an IQ less than 130 is 0.9332

For given question,

We have been given adults IQ scores that are normally distributed with a mean of μ = 100 and a standard deviation σ = 15.

We need to find the probability that a randomly selected adult has an IQ less than 130

Sketch the curve.

The probability that X < 130 is equal to the area under the curve which is less than X = 130

Since μ = 100 and σ = 15 we have:

⇒ P ( X < 130 ) = P ( X- μ < 130 - 100 )

⇒ P ( X < 130 ) = P((X− μ)/ σ < 130 - 100/20 )

Since (X-μ)/σ = Z and (130 - 100)/20 = 1.5 we have:

P (X < 130) = P (Z < 1.5)

Now, we use the standard normal table to conclude that:

P (Z < 1.5) = 0.9332

Therefore, the probability that a randomly selected adult has an IQ less than 130 is 0.9332

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