A car manufacturer advertises that its new ultra-green car obtains an average of 100 miles per gallon (mpg) and, based on its fuel emissions, is one of the few cars that earns an A+ rating from the Environmental Protection Agency. Jared Beane, an analyst at Pinnacle Research, records the mpg for a sample of 25 ultra-green cars after the cars were driven equal distances under identical conditions. Table 8.1 shows each cars mpg.

Summary Statistics (Given Information)

Mean = 96.52

Std Dev = 10.69704

Std Err Mean = 2.139408

Upper 90% Mean = 100.18027

Lower 90% Mean = 92.859725

N = 25

Frequencies (Given Information)

18 / 25 = .72 --> 18 cars out of 25 cars get less than 100 mpg --> (not given but put the numbers into words)

7 / 25 = .28 --> 7 cars out of 25 cars get greater than or equal to 100 mpg --> (not given but put the numbers into words)

.72 + .28 = 1.00 AND 18 + 7 = 25

QUESTION: How did they solve the Upper 90% Mean and the Lower 90% Mean to get the answers given above?

TABLE 8.1 97 87 MPG for a Sample of 25 "Ultra-Green" Cars 93 79 94 96 101 97 78 83 96 102 113 112 98 82 90 92 113 89 96 98