The time until recharge for a battery in a laptop computer u

The time until recharge for a battery in a laptop computer under normal conditions is normally distributed with a mean of 260 minutes and a standard of 50 minutes. (a) What ?s the probability that a battery lasts more than four hours? (b) What are quartiles (the 25% and 75% values) of battery life ? (c) What value of life in minutes is exceeded with 95% probability?

Solution

Normal Distribution
Mean ( u ) =260
Standard Deviation ( sd )=50
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
1)
P(X > 240) = (240-260)/50
= -20/50 = -0.4
= P ( Z >-0.4) From Standard Normal Table
= 0.6554                  
2)
25% is
P ( Z < x ) = 0.25
Value of z to the cumulative probability of 0.25 from normal table is -0.674
P( x-u/s.d < x - 260/50 ) = 0.25
That is, ( x - 260/50 ) = -0.67
--> x = -0.67 * 50 + 260 = 226.3  

75% is
P ( Z < x ) = 0.75
Value of z to the cumulative probability of 0.75 from normal table is 0.674
P( x-u/s.d < x - 260/50 ) = 0.75
That is, ( x - 260/50 ) = 0.67
--> x = 0.67 * 50 + 260 = 293.7  

3)
P ( Z > x ) = 0.95
Value of z to the cumulative probability of 0.95 from normal table is -1.64
P( x-u/ (s.d) > x - 260/50) = 0.95
That is, ( x - 260/50) = -1.64
--> x = -1.64 * 50+260 = 177.75