Question: The Environmental Protection Agency evaluates new car models to determine if their exhaust contains safe levels of carbon monoxide. Naturally their equipment is not perfectly precise, repeated measurements on the same car have standard deviation s = 0.5. The maximum allowed level of carbon monoxide is 1.8 ppm.

a) Suppose that 36 measurements are taken on one car and the sample mean of these 36 measurements is \[\bar{X}=1.67\]. Find the margin of error and construct a 95% confidence interval for the population mean, m. (m can be thought of as the average of a long sequence of measurements on the same car.)

b) Based on the 36 measurements can the EPA be confident that the car is below the maximum allowed level?