# Statistical Measurements and Graph

This problem has to do with graphical plotting and calculation for certain distribution. Please outline a detailed response to the questions listed with appropriate graphical and statistical data representation(s).

NB. The 90 percent confidence interval is for both the mean and for the variance too.

1. The following are the spark plug gaps, in mm, of eight spark plugs in a package (drawn from a normally distributed population): 2.50, 2.52, 2.48, 2.53, 2.47, 2.51, 2.50 and 2.55

Find a 90% percent confidence interval for all spark plug gaps (use chi-square distribution).

2. A six-cylinder, 4000-hp marine diesel engine has six fuel injectors. Because heavy fuel oil is used, the injectors get dirty after approximately 1000 hours. Consequently, pressure adjustment is lost, resulting in poor combustion and possible component failure. Assume that the chance of an injector failing is 1 in 200 after the 1000 hours of operation. Assume that the occurrences of failure of the injectors are independent of each other and that the engine can run if more than three injectors keep operating. What is the probability of the engine failing after 1000 hours of operation (use binomial distribution)?

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#### Solution Preview

See attachment please.

1. The following are the spark plug gaps, in mm, of eight spark plugs in a package (drawn from a normally distributed population): 2.50, 2.52, 2.48, 2.53, 2.47, 2.51, 2.50 and 2.55

Find a 90% percent confidence interval for all spark plug gaps (use chi-square distribution).

Solution. Denote the sample mean by and denote the sample standard deviation by s. Denote the population mean by and denote the sample standard deviation by . Note that the sample size is n=8. Use Excel, we get the following table.

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#### Solution Summary

The solution answers the questions step-by-step equationally and includes a reference, all in an attachment.