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.

The required probability is 0.6517

Step-by-step explanation:

Consider the provided information.

North Catalina State University's students can be approximated by a normal model with mean 130 and standard deviation 8 points.

μ₁ = 130 and σ₁ = 8

Chapel Mountain University's students can be approximated by a normal model with mean 120 and standard deviation 10 points.

μ₂ = 120 and σ₂ = 10

As both schools have IQ scores which is normally distributed, distribution of this difference will also be normal with a mean of μ₁-μ₂ and standard deviation will be

Therefore,

μ = 130-120=10

Now determine the probability of North Catalina State University student's IQ is at least 5 points higher than the Chapel Mountain University student's IQ:

Now by using the z table we find the z- score of -0.39 is 0.6517.

Hence, the required probability is 0.6517

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