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# Standard Deviation of the distribution

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The expected value of an investment is \$25,000.00. The standard deviation of the distribution is \$4000. In what range can we expect the actual outcome of the investment to fall with 95% certainty?

https://brainmass.com/economics/microeconomics/standard-deviation-distribution-investment-200321

#### Solution Preview

In this problem, we need to calculate the 95% confidence interval for the population mean.

The 95% ...

#### Solution Summary

The standard deviation of the distribution of an investment is examined. Neat and step-wise solution is provided.

\$2.19

## Sampling Distribution, Mean and Standard Deviation

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1) A manufacturer of paper used for packaging requires a minimum strength of 20 pounds per square inch. To check on the quality of the paper, a random sample of 10 pieces of paper is selected each hour from the previous hour's production and a strength measurement is recorded for each. The standard deviation &#963; of the strength measurements, computed by pooling the sum of squares of deviations of many samples, is know to equal 2 pounds per square inch, and the strength measurements are normally distributed.

a) What is the approximate sampling distribution of the sample mean of n = 10 test pieces of paper?
b) If the mean of the population of strength measurements is 21 pounds per square inch, what is the approximate probability that, for a random sample of n = 10 test pieces of paper, ¯x < 20?
c) What value would you select for the mean paper strength &#956; in order that P (¯x < 20) be equal to .001?

2) Suppose a random sample of n = 25 observations is selected from a population that is normally distributed, with mean equal to 106 and standard deviation equal to 12?
a) Give the mean and standard deviation of the sampling distribution of the sample mean ¯x.
b) Find the probability that ¯x exceeds 110
c) Find the probability that the sample mean deviates from the population mean &#956; = 106 by no more than 4.

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