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