Making tablets. A pharmaceutical manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The force in kilograms (kg) applied to the tablets varies a bit, with the N(11.5, 0.2) distribution.

The process specifications call for applying a force between 11.2 and 12.2 kg.

(a) What percent of tablets are subject to a force that meets the specifications?

(b) The manufacturer adjusts the process so that the mean force is at the center of the specifications, μ = 11.7 kg. The standard deviation remains 0.2 kg. What percent now meet the specifications?

Miles per gallon. In its Fuel Economy Guide for 2008 model vehicles, the Environmental Protection Agency gives data on 1152 vehicles. There are a number of outliers, mainly vehicles with very poor gas mileage. If we ignore the outliers, however, the combined city and highway gas mileage of the other 1120 or so vehicles is approximately Normal with mean 18.7 miles per gallon (mpg) and standard deviation 4.3 mpg. Exercises 3.35 to 3.38 concern this distribution.