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# expected value, standard errors of the mean (probability)

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N=36
stand. dev. is 3
mean = 5
What is the expected value?
What is the probability that the sample mean will be at least 4?
What is the probability that the sample mean will be at least 5.90?

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#### Solution Preview

<br>a) Using the Central Limit theorem, we can say that for this reasonably large size sample, the population mean is roughly equal to sample mean and hence the Expected Value = mu = 5
<br>
<br>Standard deviation of the sample means = Standard error = SE = Sigma/sqrt(n) = 3/sqrt(36) = 0.5
<br>
<br>probability that the sample mean will be at least ...

#### Solution Summary

n=36
stand. dev. is 3
mean = 5
What is the expected value?
What is the probability that the sample mean will be at least 4?
What is the probability that the sample mean will be at least 5.90?

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