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.
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.