Question 133415
1)The score on the entrance test for a well known law school has a mean score of 200 points and a standard deviation of 50 points. At value should the lowest passing score be set if the school wishes only 2.5% of those taking the entrance test to pass? and ....
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You only want the upper 2.5% of the tests to pass.
Find the z-value associated with the upper 2.5% of a normal distribution.
Use your z-table or InvNorm on your TI calculator to find z = 1.9599
Now find the x-score that corresponds to that z-score where:
z(x) = (x-mu)/sigma
1.9599 = (x-200)/50
x-200 = 97.998
x = 297.998
Rounding up you get a score of 298
Only 2.5% of the scores will be above 298.
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2)A tire manufacturer wishes to investigate the thread life of its tires. A sample of 10 tires driven 50,000 miles revealed a sample mean of 0.32 inches of thread remaining with a standard deviation of 0.09 inches. Construct a 95% confidence interval for the population mean.
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E = 1.96*0.09/sqrt(10) = 0.0558
C.I. = (0.32-0.0558,0.32+0.0558)
C.I: 0.2642 < mu < 0.3758
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Would it be reasonable for the manufacturer to conclude that after 50,000 miles the population mean amount of thread remaining is 0.30 inches?
He could have 95% confidence that the mean amt. of tread is BETWEEN
0.2642 and 0.3758, not that the mean amount is any particular
value in that range.
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Cheers,
Stan H.



 I'm really confussed and is in great need of help.