Question

the Environmental Protection Agency measures a mean gas mileage for recently tested cars as 24.8 mpg with a standard deviation of 6.2 mpg. The dataset on Fuel economy in StatCrunch gives an average of 24.2 mpg with a standard deviation of 6.5 mpg. Joe’s car is estimated at 30 mpg.

(a)   Calculate the z-scores to find the relative tab at both sources (the Exercise and the Dataset).

(b)   Relative to the other cars, with which source will Joe have the highest mpg? These next questions focus on the Dataset. Assume a normal model and use the calculator functions normalcdf and InvNorm.

(c)   What percent of cars had a measure less than 20 mpg?

(d)   What percent of cars had a measure of more than 30 mpg?

(e)   What percent of cars had a measure between 25 and 28 mpg?

(f)   Joe’s wife Ann is in the market for a new car. She hopes that she can get a car in the top 10% of mileage. How many mpg or higher will she need for her next car?

(g)   In actual dollars, what is the IQR for mpg measure? (Hint: Between what two percent is the IQR)?

I want only e,f,g questions answer, here is a to d question answers

A) mean=24.8

     Std 6.2

                      Data set

Mean 24.2

Std 6.5

Z-scores= X-mean/std

                  30-24.8/6.2

               =0.8387 The exercise

Z-scores=30-24.2/6.5

             =0.8923

B) Joe will have highest mg at dataset because 0.8923>0.8387

C)P(X<20)       

P(X-mean)/std(20-mean)/std

   P(Z<20-24.2/6.5)

P(Z<-0.6462)

Using normal table we have 0.25785

Thus 55.785%of cars had a measure as les than 20mpg

D) P(x>20)

P(X-mean/std)>30-mean/std

P(Z>30-24.2/6.5)

P(Z>0.8923)

0.1867

Thus 18.67% of cars had a measure of more than 30mpg

Answer 1