The lifetime of light bulbs produced by a company are indepe

The lifetime of light bulbs produced by a company are independent and distributed with a normal distribution with mean 1500 hours and standard deviation 125 hours. Calculate the probability that a light bulb stops working between 1400 hours and 1800 hours. If ten new light bulbs is installed and turned on at the same time, calculate the probability that all ten bulbs are still working after 1800 hours.

Solution

Normal Distribution
Mean ( u ) =1500
Standard Deviation ( sd )=125
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 1400) = (1400-1500)/125
= -100/125 = -0.8
= P ( Z <-0.8) From Standard Normal Table
= 0.21186
P(X < 1800) = (1800-1500)/125
= 300/125 = 2.4
= P ( Z <2.4) From Standard Normal Table
= 0.9918
P(1400 < X < 1800) = 0.9918-0.21186 = 0.7799                  

b)
P(X > 1800) = (1800-1500)/125
= 300/125 = 2.4
= P ( Z >2.4) From Standard Normal Table
= 0.0082