The average number of days between power outages that affect

The average number of days between power outages that affect QVT Corp. is 100 days.The standard deviation is 5 days. Assume a normal distribution. what are the chances that the number of days between outages will less than 112 days? More than 96 days? Between 96 and 112 days?

Determine the number of days, for which the probability of an outage is 0.85

Solution

Normal Distribution
Mean ( u ) =100
Standard Deviation ( sd )=5
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X < 112) = (112-100)/5
= 12/5= 2.4
= P ( Z <2.4) From Standard Normal Table
= 0.9918                  
b)
P(X > 96) = (96-100)/5
= -4/5 = -0.8
= P ( Z >-0.8) From Standard Normal Table
= 0.7881                  
To find P(a < Z < b) = F(b) - F(a)
c)
P(X < 96) = (96-100)/5
= -4/5 = -0.8
= P ( Z <-0.8) From Standard Normal Table
= 0.21186
P(X < 112) = (112-100)/5
= 12/5 = 2.4
= P ( Z <2.4) From Standard Normal Table
= 0.9918
P(96 < X < 112) = 0.9918-0.21186 = 0.7799                  
d)
P ( Z > x ) = 0.85
Value of z to the cumulative probability of 0.85 from normal table is -1.04
P( x-u/ (s.d/sqrt(n) ) > x - 100/ (5/sqrt(1) ) = 0.85
That is, ( x - 100/ (5/sqrt(1) ) = -1.04
--> x = -1.04 * 5/sqrt(1) + 100 = 94.82