NORMAL Distribution

Question 1

What are distinctive festures if a normal distribution curve

Discrete or CONTINOUS?

Thus what type of data is used normally

Answer 1

Symmetrical, bell curve shape, with most of the population falling in the middle category section

This is a CONTINOUS curve, so works with heights etc

Question 2

Where is line of symmetry and where are the two non stationary point of inflection?

Answer 2

At x = mew

and the point of inflections are always ONE STANDARD DEVIATION + OR - FROM THE MEAN

Question 3

What does finding the probability using a normal curve actually do with the curve

Answer 3

Basically find the area of the curve between your boundaries

Question 4

How to do inverse normal if your given p x > than something

Answer 4

Can use wacky calc

OR, you know p x > a is 0.2, then that means p x<a =0.9 (by probability rules)

So just do that and work it out

Question 5

What is the standard normal distribution and how to standardise your variable (find Z score)

Can you have negative vakues here!

Answer 5

This is the normal distribution with mean 0 and standard deviation of 1)
(Thus on the curve csn have negative, use this to remember the order of 0 and 1)

Z= x - U/ sigma

Question 6

If they ask you to sketch two normal curves next to each other what to do
1) to determine rough width
2) to determine the heights of the curved (+ why are the heights different)

Answer 6

1) for the widths, we know that 99.7% of data is within 3 standard deviation from mean . Thus if we calculate these values, we can roughly start and finish out curves here
2) the heights must be different, because the area under each curve IS ALWAYS = 1, so if one has a larger standard deviation, then height of mean must be less to allow for area to be one

To calcualte height, go on normal PD, and type in values for mean as X. Then roughly draw

Question 7

What does transformijg to z score allow you to do, and why was this done

Answer 7

Because finiding areas were very long, they standardised it ti get that normal curve and had values for each value in a table

Bsdicslly transforming to Z score tells you how many standard deviations you are from the mean for the ordinary curve AND THE standard curve

So p x<80 for 80, 4 square is the same as p Z<0 for 0,1

Both cases it just means you are 0 standard deviations away from the mean, and by using z score in the past it was easier, but still has use now

Question 8

When trying to find probability for normal on calculator, what tk be wary of for the LOWER BOUND

Answer 8

Need to put a value so far away so that the data is practically the same

If using standard, this may mean - infinity

Probably safest option is to do negative infinity each time

Question 9

What is the probability of any CONTINOUS distribution of say 81 so an exact value and why

Answer 9

An exact value = 0

This is because the chance of getting exact on a conitout spectrum is nothing

And on a graph the area of a line is 0

Question 10

Why is less than = basically the same as less than in this case?

Answer 10

We said probability of = something discrete is 0 so it’s gonna be the same thing !

Question 11

How to use simultaneous equation and standard normal to find the mean and sigma of a question

How to check

Answer 11

Basically we know the areas and key factor is these areas are the SAME FOR THE STANDARD NORMAL
- so if we inverse on the standard normal, we get a z score
- can now write an equation

Do this again, will have 2 simualtnous

Solve

Also check if these values return the others!

Question 12

Watch out for normal to BINOMIAL problems, what to look out for

Answer 12

First part find the probability calm

Second part, if there’s a fixed n, and obviously these won’t have different probabilities, assume they are idnepdnent, and as there is two outcomes which is fixed a BINOMIAL DISTRUBTION is valid, use it to find the answer

Question 13

Normal to histogram

Answer 13

Come back

Question 14

Why would we want to model a binomial distribution as a normal?
1) data Waise
2) CALCULATOR WISE
2 IMPORTANT

Answer 14

Potnetially because we want to see it on a CONTINOUS scale the data being represented

2) IF X IS LARGE, THE NUMBER OF FACTORIALS NEEDED IS CRAZY CALCULATOR WILL DIE
- approximating as a normal is thus a more friendly way of doing it

Question 15

When modelling the binomial as a normal, how would we find the mean and variance!

REMEMBER WHAT TO DO WITH VARIANCE

Answer 15

Mean = N x P

Variance = N X p x Q
= n x (p ) x (1-p)

Sqaure rooooot variance in calculations

Question 16

Modelling a binomial as normal, we ideally want the binomial to give a symmetrical normal distribution

When does this occur

Answer 16

This occurs when p in x -B (N,p) is CLOSE TO 0.5

Bevause mean will cause it to be quite centred

Question 17

Thus what are two conditions to see if the normal distribution is an ideal fit for the binomial

IMPORTANT + LEARN

Answer 17

• if X is very large (bevause it means factorials)
• If N is close to P (bevause it means close to symmetrical )

Question 18

HOWEVER GOING FROM BINOMAIL DISCRETE TO NORMAL CONTINOUS REQUIRES CONTINUITY CORRECTION

How to do step by step
For = etc

Answer 18

1) convert to BINOMIAL FORM
2) now apply thr correction , + 0.5 whatever
If it’s = , it’s lower and HIGHER

If 9less than 9, same as =9

Question 19

How will we know when to approximate normal form binimiak and use continuity

Answer 19

This is when it looks binomial and they say APPROXIMATE

Question 20

How to kinda check ish if you’re binomial to normal is correct

Answer 20

Not the best but try it with binomial and see if you get something close enough

Question 21

2 times you use continuity correctiond

Answer 21

1) for binomial to normal
2) if the data is just discrete (test scores etc) WILL HOPEFULLY SAY ASSUME