Question

Assume that adults have IQ scores that are normally distributed with a mean of mu equals 105 and a standard deviation sigma equals 20. Find the probability that a randomly selected adult has an IQ between 91 and 119.

Answer 1

Solution :

Let X be a random variable which represents the IQ scores of adults.

Given that,

Mean (μ) = 105

Standard deviation (σ) = 20

We have to obtain P(91 < X < 119).

We know that, if X ~ N(μ, σ²) then,

Using "pnorm" function of R we get,

P(Z < 0.7) = 0.7580 and P(Z < -0.7) = 0.2420

The probability that a randomly selected adult has an IQ between 91 and 119 is 0.5160.

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