The battery in an IPOD has a runtimetime that it will need t

The battery in an IPOD has a run-time(time that it will need to be recharged) that is normally distributed with a mean of 6 hours and a standard deviation of 30 minutes.

What percentage of these batteries must be recharged in fewer than 5 hour (have run times less than 5 hours)?

The third quartile for this run time distribution is (value)?

Solution

Mean ( u ) =180
Standard Deviation ( sd )=30
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)P(X < 150) = (150-180)/30
= -30/30= -1
= P ( Z <-1) From Standard Normal Table
= 0.1587                  
b)
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 - 180/30 ) = 0.75
That is, ( x - 180/30 ) = 0.67
--> x = 0.67 * 30 + 180 = 200.22