Express Courier Service has determined that the delivery tim

Express Courier Service has determined that the delivery time (x) for packages is normally distributed with mu = 14 hours and sigma = 2 hours. Find the percentage of packages for which delivery time is 16 hours or more. Find the guaranteed delivery time Xo, in order to be 90% sure that that packages will be delivered within the guaranteed time. Z = X- M/ sigma p(x GE 16)= p(z GE 16 - 14/2) = p(z GE 1) = 1 - 0.8413 = 0.1587 ~~16%

Solution

Normal Distribution
Mean ( u ) =14
Standard Deviation ( sd )=2
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X < 16) = (16-14)/2
= 2/2= 1
= P ( Z <1) From Standard Normal Table
= 0.8413                  
P(X > = 16) = (1 - P(X < 16)
= 1 - 0.8413 = 0.1587                  

15.87% ~ 16% are more
b)
P ( Z < x ) = 0.9
Value of z to the cumulative probability of 0.9 from normal table is 1.282
P( x-u/s.d < x - 14/2 ) = 0.9
That is, ( x - 14/2 ) = 1.28
--> x = 1.28 * 2 + 14 = 16.564