# Normal Distribution Question

Could someone go over these calculations and tell me where I'm going wrong please. It's to do with normal distribution.

The question: In a factory, the packets of sweets produced are supposed to contain 1kg each. It has been found that the weights are normally distributed with mean 1.01kg and standard deviation 0.009kg. Find, to 1 d.p, the percentage of packets above the nominal 1kg weight.

So I need to find $P(Z>1)$

If I put it into the formula I get:

$$Z = \frac{1 - 1.01}{0.009}$$ $Z = - 1.1$ recurring

And I get a bit stuck here because to use my normal distribution chart, I need to make it so $P(Z < z)$, but its $P(Z > z)$ at the moment. Therefore I would just do $1 - P(Z < z)$. However, it's also a negative so I would have to do $1-P(Z < z)$ again.

Any help would be much appreciated!

• Note that $1-(1-p)=p$ – preferred_anon Nov 11 '12 at 19:16

You want $\Pr(Z \gt -a)$, where $a$ is a positive constant. By symmetry of the standard normal, $$\Pr(Z\gt -a) =\Pr(Z\lt a).$$ This should be directly available from your tables for the cdf of the standard normal.