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# Mean of Occurring Population

The mean of a population is 76 and the standard deviation is 14. The shape of the population is unknown. Determine the probability of each of the following occuring from this population.

a. A random sample of size 35 yielding a sample mean of 79 or more

b. A random sample of size 140 yielding a sample mean of between 74 and 77

c. A random sample of size 219 yielding a sample mean of less than 76.5

#### Solution Preview

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The mean of a population is 76 and the standard deviation is 14. The shape of the population is unknown. Determine the probability of each of the following occuring from this population.

a. A random sample of size 35 yielding a sample mean of 79 or more

We can use the law of Large Numbers. Denote by Xbar the sample mean with sample size n=35. Then Xbar ...

#### Solution Summary

The shape of the population is unknown. The probability is determined for multiple random samples.

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