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Probability of Sample Mean

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Jim Sears manufactures farm equipment. His work requires the use of steel bars which must have a mean length of at least 50 inches. The bars can be purchased from a supplier in Kansas City whose bars average only 47 inches with a standard deviation of 12 inches, or from a supplier in Dallas whose bars average 49 inches with a standard deviation of 3.6 inches.

If Sears is to buy 81 bars from Kansas City, what is the probability they will have a mean of at least 50 inches? (Show calculations)

If Sears is to buy 81 bars from Dallas, what is the probability they will have a mean of at least 50 inches? (Show your calculations)

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Jim Sears manufactures farm equipment. His work requires the use of steel bars which must have a mean length of at least 50 inches. The bars can be purchased from a supplier in Kansas City whose bars average only 47 inches with a standard deviation of 12 inches, or from a supplier in Dallas whose bars average 49 inches with a standard deviation of 3.6 inches.

If Sears is to buy 81 bars from Kansas City, what is the probability they will have a mean of at least 50 inches? ...

Solution Summary

Calculates probability of sample mean.

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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 σ 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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