Verify the identity
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Answer:
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: