Question

A company selling light bulbs claims in its advertisements that its light bulbs’ average life is 1000 hours. In fact, the life span of these light bulbs is normally distributed with a mean of 1000 hours and a standard deviation of 100 hours.Find the probability that a randomly chosen light bulb will last less than 900 hours.

Answer 1

The probability that a randomly chosen light bulb will last less than 900 hours is 0.1587.

Explanation:

The life span of these light bulbs is normally distributed with a mean of 1000 hours and a standard deviation of 100 hours

Mean =
`\mu = 1000 hours`

Standard deviation =
`\sigma = 100 hours`

We are supposed to find the probability that a randomly chosen light bulb will last less than 900 hours.i.e. P(x<900)

So,
`Z=(x-\mu)/(\sigma)`

`Z=(900-1000)/(100)`

Z=-1

P(x<900)=P(z<-1)=0.1587

Hence the probability that a randomly chosen light bulb will last less than 900 hours is 0.1587.