Question

Suppose that the distribution of IQ's of North Catalina State University's students can be approximated by a normal model with mean 130 and standard deviation 8 points. Also suppose that the distribution of IQ's of Chapel Mountain University's students can be approximated by a normal model with mean 120 and standard deviation 10 points. Question 1. You select a student at random from each school. Determine the probability that the North Catalina State University student's IQ is at least 5 points higher than the Chapel Mountain University student's IQ. [View this video starting at about the 7:00 minute mark or see this page].

Answer 1

Answer:

The probability hat the North Catalina State University student's IQ is at least 5 points higher than the Chapel Mountain University student's IQ is P=0.65.

Step-by-step explanation:

To solve this problem we define a new variable X which is equal to the difference between the North Catalina State University students IQ random variable and the Chapel Mountain University students IQ random variable.

$X=X_{NC}-X_{CM}$

X will be a random variable too, approximated by a normal distribution with these parameters:

$\mu_X=\mu_{NC}-\mu_{CM}=130-120=10\\\\\sigma_X=\sqrt{\sigma_{NC}^2+\sigma_{CM}^2}=\sqrt{8^2+10^2}=\sqrt{164}= 12.8$

The probability hat the North Catalina State University student's IQ is at least 5 points higher than the Chapel Mountain University student's IQ is equivalent to the probability that X>5.

$P(X>5)=P(z>\frac{5-10}{12.8})=P(Z> -0.39)=0.65173$