# Normal distribution

• January 5th 2007, 01:21 AM
vicky86
Normal distribution
Hi! I really, really need some help with a question on an assignment i have to do for quantitative analysis. The question is as follows: "What is the chance that a sample of 5 pies will have a mean less than 275 gm given the current machine setting?"
The machine setting is to produce pies with a mean weight of 285 gms. The standard deviation is 5 gms and weights are normally distributed. The probability of one pie being under 275 gms is 2.28% and there are 12,000 pies in one group from which a sample is taken.
Pleeeease could someone help me out with this?
/Vicky
• January 5th 2007, 03:56 AM
CaptainBlack
Quote:

Originally Posted by vicky86
Hi! I really, really need some help with a question on an assignment i have to do for quantitative analysis. The question is as follows: "What is the chance that a sample of 5 pies will have a mean less than 275 gm given the current machine setting?"
The machine setting is to produce pies with a mean weight of 285 gms. The standard deviation is 5 gms and weights are normally distributed. The probability of one pie being under 275 gms is 2.28% and there are 12,000 pies in one group from which a sample is taken.
Pleeeease could someone help me out with this?
/Vicky

The mean $m$ of a sample of size $N$ taken from a population $\sim N(\mu,\sigma^2)$ has a $N(\mu,\sigma^2/N)$ distribution. Hence $\overline{m}=\mu=285$ and the standard deviation of $m$ is $\sigma/\sqrt{N}=\sqrt{5}$ So the $z$ score corresponding to $m=275$ is:

$z=\frac{275-285}{\sqrt{5}}=10/\sqrt{5}\approx -4.47$

which is off the bottom of my normal distribution table so the reqired probability is essentialy $0$.

RonL