4. (5 points) A civil engineer is analyzing the compressive strength of concrete. Compressive strength is normally distributed with o' =1000 psi . A random sample of 12 specimens has a mean compressive strength of x =3250 psi. Construct a 95% two-sided confidence interval on mean compressive strength. Comment on whether a 99% two-sided confidence interval would be wider or narrower than the one you found.5. An article in the Journal of Composite Materials (December 1989, Vol. 23(12}, pp. 12001215) describes the effect of delamination on the natural frequency of beams made from composite laminates. Five such delaminated beams were subjected to loads, and the resulting frequencies (in hertz) were as follows: 230.66, 233.05, 232.58, 229.48, 232.58, 230.66, 233.05, 232.58, 229.48, 232.58 a. (5 points) Check the assumption of normality in the population. Show work to support your conclusion. b. (5 points) Calculate a 90% two-sided confidence interval on mean natural frequency. An article in The Engineer (\"Redesign for Suspect Wiring,\" June 1990) reported the results of an investigation into wiring errors on commercial transport aircraft that may display faulty information to the flight crew. Such a wiring error may have been responsible for the crash of a British Midland Airways aircraft in January 1989 by causing the pilot to shut down the wrong engine. Of 1600 randomly selected aircraft, 8 were found to have wiring errors that could display incorrect information to the ight crew. a. (5 points] Find a 95% confidence interval on the proportion of aircraft that have such wiring errors. b. (5 points] Suppose that you use the information in this example to provide a preliminary estimate of p. How large a sample would be required to produce an estimate ofp that we are 95% confident differs from the true value by at most 0.008