S1- Help :(

Can someone please help me with S1, I just cannot get it into my head!

Firstly, can someone please explain when I can use the fomula (A U B) = P(A) + P(B) - P(A n B)? Can I use it when the data is independent/ mutually exclusive? And how do I find P(A u B) or P(A n B) when the data is independent or when it is mutually exclusive?

And can someone please explain the normal distribution to me? I cannot for the life of me understand what the heck it is! The answers I get are always totally off the mark from what the real answer should be.

For example, can someone go through these two questions with me (step by step if poss :redface:

), and how I would work it out?

1. The weights of steel sheets produced by a plant are known to be normally distributed, with mean 31.4kg and standard deviation 2.4kg. Find the percentage of sheets that wrigh more than 35.6kg.

2. The thickness of some sheets of wood follows a normal distribution with mean mew and standard deviation sigma. 96% of the sheets will go through an 8mm gauge while only 1.7% will go through a 7mm gauge. Find mew and sigma.

Sorry this post is so long; any help at all would be much appreciated. I need some urgent help, or I'll totally fail S1. Help please!

EDIT: (Last ND question, I promise!)

3. Batteries for a radio have a mean life of 160 hours and a standard deviation of 30 hrs. Assuming the battery life follows a Normal Distribution, calculate:

a) The proportion of batteries which have a life of between 150 hrs and 180 hrs.

b) The range (symmetrical about the mean) within which 75% of the batteries lie.

Thankyou so much in advance!

Reply 1

TheDuck

The normal distribution is simply a model used to predict the probabilty of things - presumably you've seen the bell-shaped normal distribution curve. The curve suggests that half of the things are below the mean (the middle of the curve is the mean) and half are above...and most of the data is around the mean....and the slope gets shallower and shallower...so although there is very little away from the mean, there are some points still. A good example of a normal distribution would be height say. Most of the data is around the mean and as we move away from the mean, there are fewer and fewer people at each height.

In your statistics, there's a good way to work out the probabilities of various things. It's call the Z-statistic and basically if X is normally distributed with mean mu and variance sigma^2, then Z=(X-mu)/sigma
and Z is normally distributed with mean 0 and variance 1. Why do we do this? Well in your textbook there should be "normal distribution tables for various z-statistics"
So if we get a z-value of 1.96 (I think it is), then if you look that up in your table you should get a value of around 0.95...that value means that the probability of something being smaller than or equal to 1.96 is 0.95.
If you wanted to know the probability of something being larger than 1.96, then you would have to do 1-0.95=0.05.

Now let's take a look at a question

Vegetto

1. The weights of steel sheets produced by a plant are known to be normally distributed, with mean 31.4kg and standard deviation 2.4kg. Find the percentage of sheets that wrigh more than 35.6kg.

1. Mu=31.4, sigma=2.4
So we convert this to a z-statistic
Z=(35.6-31.4)/2.4
=4.2/2.4
=1.75
You then have to look up the probability value for 1.75 ( I don't have the tables so I can't).
That value is the probability that the sheets are as heavy or lighter than 35.6. So, in order to find the value you're looking for, simply do 1-that as that is the probabilith that the sheets are not lighter (i.e. that they weigh more).

Reply 2

Riquelminho

Thanks, but if the question gives you the standard deviation, aren't you supposed to square root it? because the formula is (X- mu)/ sigma (variance). Or do we use the standard deviation?

Reply 3

TheDuck

Vegetto

Thanks, but if the question gives you the standard deviation, aren't you supposed to square root it? because the formula is (X- mu)/ sigma (variance). Or do we use the standard deviation?

the standard deviation squared is the variance.

So if you're given the variance, you should square it. But if you're given the standard deviation, you have what you want already.