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# population and standard deviation

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6.16
A population has distribution of unknown shape. The mean of the population is 3,500, and the standard deviation is 600.
a. If a sample of 100 values is selected randomly from this population, what is the probability that the sample mean will exceed 3,600?
b. If a sample of 200 is selected from the population what is the probability that the sample mean will exceed 3,600?
c. Compare your answer to parts a and b and explain why the two probabilities are different.

6.11
A population is normally distributed, with a mean of 1,000 and a standard deviation equal to 200.
a. Determine the probability that a random sample of size 5 selected from this population will have a sample mean less than 970?
b. Referring to part a, suppose a second sample of size 10 is selected. What is the probability that this sample will have a mean that is less than 970?
c. Why are the answers to parts a and b different? Discuss

6.17
A random sample of 100 items is selected from a population of size 350. What is the probability that the sample mean will exceed 200 if the population mean is 195 and the population standard deviation equals 20? Hint, use the finite correction factor, because the sample size is more than 5% of the population size!