Assume that the hourly cost to operate a commercial airplane

Assume that the hourly cost to operate a commercial airplane follows the normal distribution with a mean of $5,870 per hour and a standard deviation of $417.

What is the operating cost for the lowest 5% of the airplanes? (Round z value to 2 decimal places and round final answer to nearest whole dollar.)

Solution

Normal Distribution
Mean ( u ) =5870
Standard Deviation ( sd )=417
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P ( Z < x ) = 0.05
Value of z to the cumulative probability of 0.05 from normal table is -1.645
P( x-u/s.d < x - 5870/417 ) = 0.05
That is, ( x - 5870/417 ) = -1.64
--> x = -1.64 * 417 + 5870 = 5184.035 ~ 5184