Question

Intelligence quotients​ (IQs) measured on the Stanford Revision of the Binet Simon Intelligence Scale are normally distributed with a mean of 100 and a standard deviation of 16. Determine the percentage of people who have an IQ between 115 and 140.

Answer 1

Answer:

the percentage of people who have an IQ between 115 and 140 is 16.79%

Step-by-step explanation:

From the information given:

We are to  determine the percentage of people who have an IQ between 115 and 140.

i.e

P(115 < X < 140) = P( X  ≤ 140) - P( X  ≤ 115)

$P(115 < X < 140) = P( \dfrac{X-100}{\sigma}\leq \dfrac{140-100}{16})-P( \dfrac{X-100}{\sigma}\leq \dfrac{115-100}{16})$

$P(115 < X < 140) = P( Z\leq \dfrac{140-100}{16})-P( Z\leq \dfrac{115-100}{16})$

$P(115 < X < 140) = P( Z\leq \dfrac{40}{16})-P( Z\leq \dfrac{15}{16})$

$P(115 < X < 140) = P( Z\leq 2.5)-P( Z\leq 0.9375)$

$P(115 < X < 140) = P( Z\leq 2.5)-P( Z\leq 0.938)$

From Z tables :

$P(115 < X < 140) = 0.9938-0.8259$

$P(115 < X < 140) = 0.1679$

Thus; we can conclude that the percentage of people who have an IQ between 115 and 140 is 16.79%