# Math Help - Population and normal distribution

1. ## Population and normal distribution

A population of light bulbs has average lifetime of 600 hours and a standard deviation of 100 hours. Assume the population follows a normal distribution.

A) If you bought a four-pack of bulbs from this population, what is the probability that the average lifetime for the four bulbs is less than 500? Consider the four pack to be sample of n=4.

B) Suppose you bought a 16-paco of bulbs from this population. What is the probability that the average lifetime for the 16 bulbs is less than 500 hours? Consider the 16-pack to be your sample of n=16.

2. ## Re: Population and normal distribution

What do you need help with? What have you tried? What method are you supposed to be using?

3. ## Re: Population and normal distribution

I don't understand either of these or how to do them...

4. ## Re: Population and normal distribution

Normal distribution and central limit theory?

5. ## Re: Population and normal distribution

Originally Posted by Hornerk
Normal distribution and central limit theory?
Let

$L_k$ be the lifetime of the kth bulb. $L_k \sim Normal(600,100)$

The average lifetime is given by

$\bar{L}=\dfrac 1 4 \displaystyle{\sum_{k=1}^4}L_k$

Do you know how this weighted sum of $Normal(600,100)$ rvs is distributed?