Question

If a freshman is selected at random to become student assistant what is the probability of selecting a student with an IQ between 90 and 120

Answer 1

The office for admission of XYZ University found out that the IQ of incoming 1200 freshmen normally distributed with a mean of 108 and a standard deviation of 10.

$$P(90<X<120)=P(X<120)-P(X\le 90)$$

$$=P(Z<\dfrac{120-108}{10})-P(Z\le\dfrac{90-108}{10})$$

$$=P(Z<1.2)-P(Z\le-1.8)$$

$$\approx0.88493-0.03593=0.8490$$