Fuel economy estimates for automobiles built one year predicted a mean of 29.2 m

Question

Fuel economy estimates for automobiles built one year predicted a mean of 29.2 mpg and a standard deviation of 4.8 mpg for highway driving. Assume that a Normal model can be applied. Use the 68-95-99.7 Rule to complete parts a) through e) b) In what interval would you expect the central 99.7% of autos to be found? using the 6895-99 7 rule, the central 99 7% of autos can be expected to be found in the interval from (Do not round. Type integers or decimals.) to mpg c) About what percent of autos should get more than 34 mpg? Using the 68-95-99.7 rule, about%of autos should get more than 34 mpg Do not round. Type an integer or a decimal.) d) About what percent of autos should get between 34 and 38.8 mpg? using the 68-95-997 rule, about 1% of autos should get between 34 and 38.8 mpg Do not round. Type an integer or a decimal.) e) Describe the gas mileage of the worst 2.5% of cars. Choose the correct answer below. OA. They get more than 34 mpg. O B. They get less than 14.8 mpg. O C. They get less than 19.6 mpg O D. They get less than 24.4 mpg Click to select your answer(s)

Explanation / Answer

Solution:- Given that mean = 29.2, sd = 4.8

b) Central 99.7% to be found with 3 standard deviations from the mean
= (29.2 +/- 3*4.8)
= (14.8 , 43.6)

c) 34 mpg = 29.2 + 4.8 = mean + 1*SD

So percentage above 34 = (100 - 68) /2 = 16%

d. 38.8 = 29.2 + (2*4.8) = mean + 2*SD

So percentage above 38 = (100 - 95) /2 = 2.5%

Between 33 and 38.8,

percentage = (100-68)/2 - (100-95)/2 = 13.5%

e. z-score = -1.96
-1.96 = (x-29.2)/4.8
x = 29.2 - (4.8*1.96)
=`19.792 mpg and lower

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