Test scores for a standardized math test follow a normal distribution with a mean of 73 and a standard deviation of 8. a random sample of 23 students took this math test. what is the probability that the average score of the 23 students falls above 75?

Solution:

We are given:

μ=73,σ=8,n=8

We have to find P(Mean >75)

To find this probability, we need to find the z score:

z=(xbar-μ)/(σ/sqrt(n))

=(75-73)/(8/sqrt(23))

=1.20

Now we have to find P(z>1.20)

Using the standard normal table, we have:

P(z>1.20)=0.1151

Therefore the probability that the average score of the 23 students falls above 75 is 0.1151

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