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].

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

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.

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