
Sampling question 2
The masses of kilogram bags of flour produced in a lottery have a normal distribution with mean 1.005 kg and standard deviation 0.0082 kg. A shelf in a store is loaded with 22 of these bags assumed to be randomn sample.
a)Find the probability that a randomly chosen bag has mass less than 1 kg.
b) Find the probability that the mean mass of 22 bags is less than 1 kg.
State giving a reason, which of the above answers would be little changed if the distribution of masses were not normal.

To find probabilities for individual members of a population use the formula:
$\displaystyle z=\frac{x{\mu}}{\sigma}$
To find probabilites for the mean of a sample size use:
$\displaystyle z=\frac{x{\mu}}{\frac{\sigma}{\sqrt{n}}}}$