5. The operations manager of a large production plant would like to estimate the mean amount of timea worker takes to assemble a new electronic component. Assume that the standard deviation of thisassembly time is 3.6 minutes.a. After observing 120 workers assembling similar devices, the manager noticed that theiraverage time was 16.2 minutes. Construct a 90% confidence interval for the meanassembly time.b. How many workers should be involved in this study in order to have the mean assemblytime estimated up to + 15 seconds with 90% confidence?6. A new rocket-launching system is being considered for deployment of small, short-range rockets.The existing system has p = 0.8 as the probability of a successful launch. A sample of 40experimental launches is made with the new system, and 34 are successful. Using 95% confidence,the confidence interval is 0.85 + 0.111. What is the sample size required @ 90% level ofconfidence?PART II. ESSAY1. What is the effect of having different levels of confidence in estimation of population mean?2. Research and make a report of the importance of confidence interval estimations in businessdecision making and engineering design.End of Exercise 2 PART I. CONFIDENCE INTERVAL ESTIMATION1. The diameter of holes for a cable harness is known to have a normal distribution with a standarddeviation of 0.01 inch. A random sample of size 10 yields an average diameter of 1.5045 inch.a. Find a 99% two-sided confidence interval on the mean hole diameter.b. Find a 90% two-sided confidence interval on the mean hole diameter.c. Explain the difference of the interval between the two confidence levels.2. An article in the Journal of Composite Materials (December 1989, Vol. 23, p. 1200) describes theeffect of delamination on the natural frequency of beams made from composite laminates. Five suchdelaminated beams were subjected to loads, and the resulting frequencies (in hertz) were as follows:230.66 233.05 232.58 229.48 232.58a. Calculate a 99% two-sided confidence interval on mean natural frequency.3. The fraction of defective integrated circuits produced in a photolithography process is being studied.A random sample of 300 circuits is tested, revealing 13 defectives.a. Calculate a 95% two-sided Cl on the fraction of non-defective circuits produced by thisparticular tool.b. Calculate a 90% upper confidence bound on the fraction of defective circuits.4. The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomlyselected parts. The sample standard deviation is s = 0.37. Construct a 95% two-sided confidenceinterval for the standard deviation

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