What is the normal distribution and how do I use it?

The normal distribution is a distribution we can use when we know the mean and the standard deviation of a population, to work out probabilities that a certain even will occur.
The main properties of a normal distribution is that it has a bell shaped curve, with the mean of the population corresponding to the x value of the curve's peak. It also has a fixed variance.
A common example of its use would be the following question:A factory is producing bags of sugar, weighed in grams. The factory wishes to know the probability that a bag of sugar weighs more than 750g. The mean of the weights is 600g, the standard deviation in 50g. Work out the probability.
A key formula for the normal distribution is the normalisation formula,
Z= (value - mean)/ standard deviation
for this example Z= (750-600)/50 = 3
When we look at the table of Z scores to probabilities we see that this relates to the probability: 0.99865
but this value only corresponds to the probability that the bag of sugar is less than 750, so we calculate
1-0.99865 = 0.00135