Question

a batch of 5000 electric lamps has a mean life of 1000 hours and a standard deviation of 75 hours. assuming a normal distribution: how many lamps will fail before 900 hours

Answer 1

$$\mu=1000, \sigma=75$$

$$z={x-\mu \over \sigma}\sim N(0,1)$$

$$x=900, z={900-1000 \over 75}={-4\over 3} \approx-1.3333$$

$$P(X<900)=P(Z<{-4\over 3})=0.09121122$$

$$n=5000\cdot0.09121122=456(lamps)$$

 456 lamps will fail before 900 hours.