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The average on a statistics test was 75 with a standard deviation of 11. If the...

The average on a statistics test was 75 with a standard deviation of 11. If the test scores are normally distributed, find the probability that the mean score of 25 randomly selected students is between greater than 82.
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Answer #1

Let , , n=25

Now , the sampling distribution of the sample mean is approximately normaly distributed with sample mean and sample standard deviation

Now ,

; From standard normal distribution table

Therefore , the probability that the mean score of 25 randomly selected students is greater than 82 is 0.0007.

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