Question

Assume that adults have IQ scores that are normally distributed with a mean of 105 and a standard deviation of 15. Find the probability that a randomly selected adult has an IQ between 92 and 118.

Answer 1

Let X be the adults IQ scores.

X is normally distributed with mean µ=105 and Standard deviation σ = 15

Now we want to find the probability randomly selected adult has IQ between 92 and 118

We will solve this problem by standardising.

P(92 < X < 118) = P((92 - 105)/15 <(X - µ)/ σ <(118- 105)/15)

                              = P(- 0.87 < Z < 0.87)

                              = 1 – 2*P(Z ≤ -0.87)

                              = 1 – 2*0.1922 …… (Using statistical table)

                              = 0.6156

P(92 <X <118) = 0.6156

The probability that a randomly selected adult has an IQ between 92 and 118 is 0.6156