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A researcher selects a sample of 49 participants from a population with a mean of 12...

A researcher selects a sample of 49 participants from a population with a mean of 12 and a standard deviation of 3.5. What is the probability of selecting a sample mean that is at least equal to the population mean? 0.50 equal to the probability of selecting a sample mean that is at most equal to the population mean all of the above none of the above

Expert Solution

Solution :

It is given that a researcher selects a sample of 49 participants from a population with a mean of 12 and a standard deviation of 3.5.

To find the probability of selecting a sample mean that is at least equal to the population mean.

Since, , thus , we can assume that is Normally Distributed. That is ,

We know that if is a Normal RV , then the Sample Mean is also Normally distributed.

Thus, we can conclude that, the probability of selecting a sample mean that is atmost equal to the population mean is also = 0.5. So the Required Answers are :

Required Probability = 0.5
equal to the probability of selecting a sample mean that is at most equal to the population mean.

Thus , the Correct Option is (C) --- All of the Above ......................................... (Ans)

milcah answered 5 months ago

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