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(b) the posterior standard deviation, and (c) the 95% confidence intervals for the mean thickness based on prior and posterior information. Does the pressure vessel meet the specification of a mean thickness of at least 628 mm using two-sided hypothesis testing with a significance level of 5%? 6-9. The air quality in a building is of interest to an environmental engineer. The mean air quality is mea- sured in the form of the amount of pollutant in the air in parts per million (ppm). The mean amount of pollutant can be assumed to have a normal probability distribution with a mean (4) and standard deviation (). The standard deviation of pollutant (a) is known to be 0.2 ppm. The air quality based on the records of the building has a mean of 3 ppm and a standard deviation of 0.2 ppm. A sample of n = 10 was collected. The sample resulted in a mean of 2.7 ppm. Determine: (a) the posterior mean pollutant concentration, (b) the posterior standard deviation, and (c) the 95% confidence intervals for the mean concentration based on prior and posterior information.