LifeCharge Batteries claims that their batteries last an ave

LifeCharge Batteries claims that their batteries last an average of 120 hours when used in a hand held gaming system, with a standard deviation of about 5 hours. An independent quality control company took a sample of 41 batteries, and used the same hand held gaming system that LifeCharge used to record the time the batteries lasted

a) What the probability that the value of the sample mean is less than 119.8 hours?

Solution

Mean ( u ) =120
Standard Deviation ( sd )=5
Number ( n ) = 41
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X < 119.8) = (119.8-120)/5/ Sqrt ( 41 )
= -0.2/0.7809= -0.2561
= P ( Z <-0.2561) From Standard NOrmal Table
= 0.3989