A certain commercial jet plane uses a mean of 0.15 gallons of fuel per passenger-mile, with a standard deviation of 0.01 gallons.

a. Find the mean number of gallons the plane uses to fly 8000 miles if it carries 210 passengers.

b. Assume the amounts of fuel used are independent for each passenger-mile traveled. Find the standard deviation of the number of gallons of fuel the plane uses to fly 8000 miles while carrying 210 passengers.

c. The plane used X gallons of fuel to carry 210 passengers 8000 miles. The fuel efficiency is estimated as X/(210 × 8000). Find the mean of this estimate.

d. Assuming the amounts of fuel used are independent for each passenger-mile, find the standard deviation of the estimate in part (c).

Answer :

Step 1 of 4 :

Given, A certain commercial jet plane uses a mean of 0.15 gallons of fuel per passenger-mile, with standard deviation of 0.01 gallons.

The claim is to find the mean number of gallons the plane uses to fly 8000 miles if it carries 210 passengers.

Let X be the number of gallons of fuel used.

The number of passengers-miles is 8000(210) = 1,680,000.

The mean is = 1,680,000 (0.15)

= 252,000 gallons.

Therefore, the mean number of gallons the plane uses to fly 8000 miles if it carries 210 passengers is 252,000 gallons.

Step 2 of 4 :

b)

We have to assume that the amount of fuel used are independent for each passenger-mile travelled.

Then the claim is to find the standard deviation of the number of gallons of fuel the plane uses to fly 8000 miles while carrying 210 passengers

We have that standard deviation 0.01 gallons

Therefore, =

=

= 129.6148 gallons

Therefore, the standard deviation of the number of gallons of fuel the plane uses to fly 8000 miles while carrying 210 passengers is 129.6148 gallons.

Step 3 of 4 :

c)

The plane used X gallons of fuel to carry 210 passengers 8000 miles.

Estimate of the fuel efficiency is X / (210 8000).

The claim is to find the mean of the estimate

The mean is = ( 1 / 1,680,000)

Where = 252,000 gallons

Substitute this to

Then, = ( 1 / 1,680,000) 252,000

= 0.15

Therefore, the mean of the estimate is 0.15.