Step 1
Now what?
The local authorities in a city installed 2000 long burning electric light globes in the street.
The globes have an average life of 1000 burning hours with a standard deviation of 200 hours.
The life of the globes is normally distributed.
Can you help me calculate the number of globes that are expected to fail in the first 600 hours??
Step 1:
Let X be the random variable lifetime of a single globe.
X ~ Normal( ).
Find Pr(X < 600) = Pr(z < -2) = p.
Step 2:
Let Y be the random variable number of globes that fail in the first 600 hours.
Y ~ Binomial(p, n = 2000)
and you've found the value of p from step 1.
Therefore E(Y) = ......