Question

The average life of a battery is 60 hours. Further, the life of the battery follows a normal distribution with standard deviation of 5 hours. As a quality control manager, your goal is to limit the production of defective products. Your company considers a defective battery to be one that lasts less than 50 hours.

Out of a batch of 100 batteries, what is the expected number of defective batteries?

Answer 1

The company considers a defective battery to be one that lasts less than 50 hours

Let X be the random variable which takes the time of last of the battery.

So from the given information X follows normal distribution with mean = = 60 hours and

standard deviation = = 5 hours

Let's find P( X < 50) using excel :

P( X < 50) = "=NORMDIST(50,60,5,1)" = 0.02275

Out of a batch of 100 batteries, what is the expected number of defective batteries?

therefore required number of defectives = 100*0.02275 = 2.275 which is approximately equal to 2.