## What is the standard deviation of the total length?

1.  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.

c.   Find the standard deviation of the number of gallons of fuel the plane uses to fly 8000 miles while carrying 210 passengers.

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

e.  The fuel efficiency is estimated as X/(210 × 8000). Find the mean of this estimate.

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

2.  Woodworkers Alex and Brandon make precision pieces for toys. Each toy requires four 8- inch long sticks. Alex cuts four sticks one at at time, and their lengths are independent. Alex's sticks have mean length 8 inches with a standard deviation 0.15 inches. Brandon clamps four sticks together and cuts them all at once, so that they all have the same length. Brandon's sticks also have a mean length of 8 inches with a standard deviation of 0.15 inches.

a.  Alex's four sticks are laid end-to-end. What is the mean of the total length?

b.  What is the standard deviation of the total length?

c.   Brandon's four sticks are laid end-to-end. What is the mean of the total length?

d.  What is the standard deviation of the total length?

e.  Four sticks, two from Alex and two from Brandon, are laid end-to-end. What is the mean of the total length?

f.     What is the standard deviation of the total length?

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