Student scores on exams given by a certain instructor have mean 74 and standard deviation 14. this instructor is about to give two exams, one to a class of size 25 and the other to a class of size 64. approximate the probability that the average test score in the class of size 25 exceeds 80.

Step-by-step explanation:

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Let X the random variable that represent the Student scores on exams given by a certain instructor, we know that X have the following distribution:

The sampling distribution for the sample mean is given by:

The deduction is explained below we have this:

Since the variance for each individual observation is then:

And then for this special case:

We are interested on this probability:

And we have already found the probability distribution for the sample mean on part a. So on this case we can use the z score formula given by:

Applying this we have the following result:

And using the normal standard distribution, Excel or a calculator we find this: