16. The Department of Transportation in a foreign county establishes gas-mileage standards that automobiles sold must meet or else a "gas guzzler II tax is imposed on the sale of the offending types of automobile.

For the "compact, 4-door" class of automobiles, the target average gas mileage is 25 miles per gallon.

Achievement of the standard is tested by randomly choosing 20 cars from a manufacturer's assembly line and then examining the distance between the vector of 20 observed measurements of gas mileage/gallon and a

(20 x 11 vector of targeted gas mileages for these cars.

Letting X represent the 20 x 1 vector of observed gas mileages, and letting t represent the 20 x 1 vector of targeted gas mileages (i.e., t = [25,25, ... , 25J'l, the distance measure is D(x, tl = [(x - t)'(x - t)F/2.

If D(x, tl ::: 6, then the type of automobile being tested is judged to be consistent with the standard; otherwise, the type of automobile will be taxed.

Specific Motors Company is introdUCing a new four-door compact into the market and has requested that this type of automobile be tested for adherence to the gas-mileage standard. The engineers at Specific Motors know that the miles per gallon achieved by their compact four-door automobile can be represented by a normal distribution with mean 25 and variance 1.267, so that the target gas mileage is achieved on average.