Question

The bulbs manufactured by a company gave a mean life of 3000 hours with standard
deviation of 400 hours. If a bulb is selected at random, what is the probability it will
have a mean life less than 2000 hours?

Answer 1

Answer on Question#39859, Math, Statistics

The bulbs manufactured by a company gave a mean life of 3000 hours with standard deviation of 400 hours. If a bulb is selected at random, what is the probability it will have a mean life less than 2000 hours?

Solution

We have:

$X =$ lifetime of bulb, Mean $(\mu) = 3000$ hours, standard deviation $(\sigma) = 400$ hours.

The probability it will have a mean life less than 2000 hours is $P(x < 2000)$.

$$Z(X) = \frac{X - \mu}{\sigma}.$$ $$Z(2000) = \frac{2000 - 3000}{400} = -\frac{1000}{400} = -2.5.$$ $$P(x < 2000) = P(Z < -2.5) = 0.0062.$$

Answer: 0.0062.