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# Using sample mean and standard deviation

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Fast Service Truck Lines uses the Ford Super Duty F-750 exclusively. Management made
a study of the maintenance costs and determined the number of miles traveled during
the year followed the normal distribution. The mean of the distribution was 60,000 miles
and the standard deviation 2,000 miles.
a. What percent of the Ford Super Duty F-750s logged 65,200 miles or more?
b. What percent of the trucks logged more than 57,060 but less than 58,280 miles?
c. What percent of the Fords traveled 62,000 miles or less during the year?
d. Is it reasonable to conclude that any of the trucks were driven more than 70,000 miles?

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#### Solution Preview

Basically, in a case like this, you want to use the fact that we have normal distribution and a mean and standard deviation to calculate a z-score, or standard normal value (page 229 of your text) for the questions in ...

#### Solution Summary

Using sample mean and standard deviation to make probablistic assessments of a data set. Practical application of z-score when assuming normal distribution of the population.

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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 &#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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