Microsoft Word - FinalExam_Fall2014ver2.docx SHOW WORK TO GET FULL CREDIT MATH 333 Final Exam December 17, 2014 Fall 2014 XXXXXXXXXXDecember 17, 2014 MATH-333 (Common Final Exam) XXXXXXXXXXNJIT Q. # 1...

Probably and Statistics Exam that covers the basics such as mean, median, mode up to hypothesis testing.


Microsoft Word - FinalExam_Fall2014ver2.docx SHOW WORK TO GET FULL CREDIT MATH 333 Final Exam December 17, 2014 Fall 2014 December 17, 2014 MATH-333 (Common Final Exam) NJIT Q. # 1 #2 #3 #4 #5 #6 #7 #8 Total 12 12 14 14 14 12 12 10 100 This is a closed book exam. Non-programmable calculator is allowed. Formula sheet and tables are provided. Name (PRINT) _______________________________________ Section # ______ Last First xxx Instructors: Egbert Ammicht, George Mytalas, Padma Natarajan, Jonathan Porus Problem 1) (Note that a) and b) are separate problems) a) The lifetime of a mechanical assembly in a vibration test is exponentially distributed with a mean of 500 hours. If an assembly has been on test for 500 hours without a failure, what is the probability of a failure in the next 100 hours? (Round your answer to 4 decimal places) (6 points) b) A metabolic defect occurs in approximately 5% of the infants born at a hospital. Six infants born at the hospital are selected at random. What is the probability that exactly two have the metabolic defect? (Round your answer to 4 decimal places) (6 points) SHOW WORK TO GET FULL CREDIT MATH 333 Final Exam December 17, 2014 Problem 2) (Note that a) and b) are separate problems) a) Suppose that a certain random variable, X, has the following cumulative distribution function (cdf): 0 x < 2="" f(x)="0.25x2" –="" x="" +="" 1="" 2="" ≤="" x="" ≤="" 4="" 1="" 4="">< x="" find="" p(x=""> 2.5) (Round your answer to 4 decimal places) (6 points) c) A soft drink dispensing machine is said to be out of control if the variance of the contents exceeds 1.15 deciliters. A random sample of 25 drinks from this machine is studied and the sample variance is computed to be 2.03 deciliters. Assume that the contents are approximately normally distributed. Construct a 90% lower confidence bound on σ2. (Round your answer to 2 decimal places) (6 points) SHOW WORK TO GET FULL CREDIT MATH 333 Final Exam December 17, 2014 Problem 3) The life length of light bulbs manufactured by a company is normally distributed with a mean of 1000 hours and a standard deviation of 200 hours. a) What life length in hours is exceeded by 97.5% of the light bulbs? (7 points) b) What is the probability that the average life length of a random sample of 36 light bulbs will exceed 1005 hours? (Round your answer to 4 decimal places) (7 points) SHOW WORK TO GET FULL CREDIT MATH 333 Final Exam December 17, 2014 Problem 4) A civil engineer is analyzing the compressive strength of concrete. Compressive strength is normally distributed with σ = 31.62 psi. A random sample of 36 specimens has a mean compressive strength of 3250 psi. a) Construct a 95% two-sided confidence interval on the mean compressive strength. (Round your answer to 3 decimal places) (7 points) b) Suppose that it is desired to estimate the compressive strength with an error of less than 15 psi at 99% confidence. σ = 31.62 psi. What sample size is required? (7 points) SHOW WORK TO GET FULL CREDIT MATH 333 Final Exam December 17, 2014 Problem 5) (Note that a) and b) are separate problems) a) An Izod impact test was performed on 16 specimens of a PVC pipe. The sample mean is 1.25 and the sample standard deviation is 0.25. Construct a 99% confidence interval on the Izod impact strength. (Round your answer to 3 decimal places) (7 points) b) Of 1000 randomly selected cases of lung cancer, 823 resulted in death within ten years. Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.03? (7 points) SHOW WORK TO GET FULL CREDIT MATH 333 Final Exam December 17, 2014 Problem 6) (Note that a) and b) are separate problems) a) As items come to the end of a production line, an inspector chooses items to undergo a complete inspection. Of all items produced, 10% are defective and the remaining good. Sixty percent of all defective items go through a complete inspection, and 20% of all good items go through a complete inspection. Given that an item is completely inspected, what is the probability that it is defective? (6 points) b) The following table displays the number of defective and non-defective medical devices produced by three manufacturing companies. Company A (A) Company B (B) Company C (C) Total Non-defective (N) 18 7 19 Defective (D) 2 3 1 50 Two medical devices are randomly selected without replacement. Find the probability that at least one of them is defective (D). (Round your answer to 3 decimal places) (6 points) SHOW WORK TO GET FULL CREDIT MATH 333 Final Exam December 17, 2014 Problem 7) A manufacturer claims that the average lifetime of cameras is more than 84