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

Answer:

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

Step-by-step 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, $Z=\frac{x-\mu}{\sigma}$

$Z=\frac{900-1000}{100}$

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.