The measure of intelligence, IQ, of a group of students is assumed to be Normally distributed with mean 100 and standard deviation 15 - Edexcel - A-Level Maths Statistics - Question 7 - 2007 - Paper 1

To find the probability that a student has an IQ less than 91, we will standardize the value using the z-score formula:

$z = \frac{X - \mu}{\sigma}$

Where:

• $X$ is the IQ value (91)
• $\mu$ is the mean (100)
• $\sigma$ is the standard deviation (15)

Calculating the z-score:

$z = \frac{91 - 100}{15} = \frac{-9}{15} = -0.6$

Next, we find the probability for z < -0.6. Using the standard normal distribution table:

• The probability for z < -0.6 is approximately 0.2743.

Therefore:

$P(X < 91) \approx 0.2743$