Distribution function question please.

[robert_robert]

Hi guys, I have this problem:

"The degree of efficiency of the solar cells produced by the company PhotoEnergy is distributed according to N(30;4). How many of the 60,000 cells produced per day have a degree of efficiency between 30% and 35%?"

So here the normal distribution has a mean of 30 (i.e the average degree of efficiency of the cells is 30%) and a variance of 4.

I'm not really sure about how to solve this question. Can you please provide me with some hints?

--What I'm thinking--:

Let X be the number of cells having a degree of efficiency between 30% and 35%.

I guess I should calculate the distribution function for the normal distribution.

I will update this part (the I'm thinking part) regularly.

[Mean Joe]

If the question instead were: "What is the probability that a single cell will have an efficiency between 30% and 35%?"

Then you know how you would use the normal tables to calculate?
eg let X be the efficiency for a single cell
P(30 < X < 35) = P(0 < Z < 1.25) = Phi(1.25) - Phi(0)

Does this look familiar?

For your problem, you'll do something similar, but have to apply the Central Limit Theorem.