# Normal Probability & Hypothesis Testing

5. The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation 2.

a. What is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.5?

b. Find an interval that includes, with probability 0.95, the average fracture strength of hundred randomly selected pieces of this glass.

c. Find n such that the probability that the average fracture strength of n randomly selected pieces of this glass exceeds 14.5 will equal to 0.95.

6. According to a survey conducted by the American Bar Association, 1 in every 410 Americans is a lawyer, but 1 in every 64 residents of Washington, D.C. is a lawyer.

a. If you select a random sample of 1500 Americans, what is the approximate probability that the sample contains at least on lawyer?

b. If the sample is selected from among the residents of Washington, D.C., what is the approximate probability the sample contains more than 30 lawyers?

c. If you stand on a Washington, D.C. street corner and interview the first 1000 persons who walked by and 30 say that they are lawyers, does this suggest that the density of lawyers passing the corner exceeds the density within the city? Explain.

Please see the attached file.

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#### Solution Summary

The solution provides step by step method for the calculation of probability using the Z score and testing of hypothesis. Formula for the calculation and interpretation of the results are also included.

Confidence Interval, Normal Probability & Hypothesis Testing

#4. you collected the following information:

n=38

x bar= 12.35

s=3.82

find the 95% confidence interval estimate for m- mule

#2. heavy duty light bulbs made by a certain company claim to have lives that are normally distributed with a mean of 5000 hours and a standard deviation of 400 hours.

A. find the probability that one of these light bulbs lasts more than 6000 hours.

B. in a box of 1000 such light bulbs, how many do you expect will last between 4900 and 5512 hours?

C.what is the 94th percentile of this distribution?

#3 .you sampled 500 BobBob GPS units and found that percisley 20 had some defect. the rest were free of defect.

A.find a 90% confidence interval estimate of the true proportion of defective BobBob GPS units. what is the margin of error in your estimate?

B.the BobBob company has claimed that less than 1% of all its units are defective. is this consistent with expectations? why or why not?

#5. given the hypothesis test

ho: p= 0.8

h1: p< 0.8

in a sample of 200 you pulled 148 successes and 52 failures. what is the result of this hypothesis test at the (a) a=0.05 (b) a=0.01 level?

#6. the power company claims that it delivers 125 volts a day to Triola's house. to test this claim. Triola sets up his own device which measures the voltage to his home. on 40 such days, he measured the voltage to his house. On these 40 days the mean voltage was 123,7 volts with a standard deviation of 0.24 volts.

B. at the a=0.01 level, test the claim that the average daily voltage is different than 125 volts.

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