1. ## 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

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

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

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

RonL