A cruising altitude, a commercial jet engine consumes an average of 945 gallons

Question

A cruising altitude, a commercial jet engine consumes an average of 945 gallons of fuel per hour with a standard deviation of 52 gal per hour. Assume that the fuel consumption follows a normal distribution at cruising altitude. Use the Z-table provided in class and round appropriately to the precision provided in the table. Determine the following values and draw a sketch labeled with the mean and point of interest and shade the area of interest to represent each. a. b. c. The probability that the hourly fuel consumption is between 800 and 1000 gallons The probability that the hourly fuel consumption is less than 950 gallons If the cost for fuel for the commercial jet engine is $0.85/gallon, and the aircraft cruises 225 hours per month, what is the probability that the monthly cost of fuel exceeds

Explanation / Answer

We use the following params to normalize the values of random variable of fuel consumption per hour.

Mean = 945
Stdev = 52

a. P(800<X<1000)
= P(800-945/52<Z<1000-945/52)
= P(-2.8<Z<1.06)
= .855-.003
= .852

b. P(X<950)
=P(Z<950-945/52)
=P(Z<.096)
=.54

c. So, $150,000 is 150000/.85 = 176470.59 gallons
Now, per hours consumption is = 176470.59 /225 = 784.32 gallons per hour

So, P(X>784.32 )
= P(Z>(784.32 -945/52)
= P(Z>-3.2)
= .000721

The chance of this happening is very less or .07%

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