Given that the scores of a set of candidates on an IQ test are normally distributed. If the I.Q. test has a mean of 100 and a standard deviation of 10, what is the probability that a candidate who takes the test will score between 90 and 110?

0.6826

The correct answer is Option (2) → 0.6826

Given $μ = 100$ and $σ =10$.

So, required probability = $P(90 < X < 110)$

$= P\left(\frac{90-100}{10}<Z<\frac{110-100}{10}\right)$

$= P(-1<Z<1)$

$= F(1) - F(-1) = F(1) - [1 − F(1)]$

$=2F(1)-1= 2 × 0.8413-1 = 0.6826$