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Rod Diameter Standard Deviation

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FIN 220 FALL 07
QUESTION 1) FROM PAST EXPERIENCE, THE POPULATION STANDARD DEVIATION OF ROD DIAMETERS PRODUCED BY A MACHINE HAS BEEN FOUND TO BE 3~ = .053 INCHES.FOR A SIMPLE RANDOM SAMPLE OF n=30 RODS/THE AVERAGE DIAMETER IS FOUND TO BE X = 1.400 INCHES.
A) WHAT IS THE PROBABILITY THAT IF A SINGLE ROD IS CHOSEN AT RANDOM FROM THE
POPULATION THAT IT WILL HAVE A DIAMETER OF BETWEEN 1.400 INCHES PLUS .106 INCHES.
B) WHAT IS THE PROBABILITY THAT IF A RANDOM SAMPLE OF n=30 IS TAKEN THAT THE SAMPLE WILL HAVE A MEAN VALUE 1.4055.
C) WHAT IS YOUR POINT ESTIMATE OF THE POPULATION MEAN.
D) WHAT IS THE 95% CONFIDENCE INTERVAL FOR THE POPULATION MEAN. (RMW)
QUESTION 2) A SIMPLE RANDOM SAMPLE OF n= 10 EMPLOYEES HAS BEEN SELECTED FROM A FIRM
IN WHICH A LARGE NUMBER OF TAX PREPARERES ARE EMPLOYED .EACH OF THE 10 PERSONS HAS
BEEN GIVEN THE SAME INFORMATION, THEN ASKED TO COMPLETE THE TAX RETURN.THE
SUMMARY RESULTS FOR THE SAMPLE ARE X = 39.42 MINUTES AND 5=13.75 MINUTES.
WHAT IS THE 99% CONFIDENCE INTERVAL FOR THE POPULATION MEAN (RMW)
QUESTION 3)
A)YOU PLAN TO ESTIMATE THE MEAN SELLING PRICE OF A COLLEGE TEXTBOOK.HOW MANY
TEXTBOOKS MUST YOU SAMPLE IF YOU WANT TO BE 95% CONFIDENT THAT THE SAMPLE MEAN IS
WITHIN \$ 2 OF THE TRUE POPULATION MEAN = jk. (MT)
B)A MEMBER OF CONGRESS WANTS TO DETERMINE HER POPULARITY IN A CERTAIN PART OF THE
STATE. SHE INDICATES THE PROPORTION OF VOTERS WHO WILL VOTE FOR HER MUST BE
ESTIMATED WITHIN + - 2 PERCENT OF THE POPULATION PROPORTION .FURTHUR THE 99%
CONFIDENCE IS TO BE USED.IN PAST ELECTIONS THE REPRESENTATIVE RECEIVED 40 % OF THE
POPULAR VOTE IN THAT AREA OF THE STATE.SHE DOUBTS WHETHER IT HAS CHANGED MUCH.HOW
MANY REGISTERED VOTERS SHOULD BE SAMPLED. . (RM)
QUESTION 4) IN A RANDOM SAMPLE, 136 OF 400 PERSONS GIVEN A FLU VACCINE EXPERIENCED
SOME DISCOMFORT.CONSTRUCT A 95% CONFIDENCE INTERVAL FOR THE TRUE PROPORTION OF
PERSONS WHO WILL EXPERIENCE SOME DISCOMFORT FROM THE VACCINE. (F+S)

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FIN 220 FALL 07
QUESTION 1) FROM PAST EXPERIENCE, THE POPULATION STANDARD DEVIATION OF ROD DIAMETERS PRODUCED BY A MACHINE HAS BEEN FOUND TO BE 3~ = .053 INCHES.FOR A SIMPLE RANDOM SAMPLE OF n=30 RODS/THE AVERAGE DIAMETER IS FOUND TO BE X = 1.400 INCHES.
A) WHAT IS THE PROBABILITY THAT IF A SINGLE ROD IS CHOSEN AT RANDOM FROM THE
POPULATION THAT IT WILL HAVE A DIAMETER OF BETWEEN 1.400 INCHES PLUS .106 INCHES.
Let Y be the ROD DIAMETERS. Then we know that Y is a random variable following roughly a normal distribution with mean 1.400 inches and standard deviation 0.053 inches. Hence, THE PROBABILITY THAT IF A SINGLE ROD IS CHOSEN AT RANDOM FROM THE POPULATION THAT IT WILL HAVE A DIAMETER OF BETWEEN 1.400 INCHES PLUS .106 INCHES is

Let Z=(Y-1.400)/0.053. Then Z follows a standard normal distribution N(0,1) roughly. Hence,
...

Solution Summary

An RTF file attached shows how to perform these statistic analyses on rods.

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