normal distribution

What is the shape of the uniform distribution?

Rectangle

What do we know about exact probilities for continuous distributions?

Why ar the mean and the median equal?

Because the mean is the middle value and so is the median

What is the shape of a normal distribution?

What are the conditions required

Bell curve

Equal Averages

Random events

Independent events

Empirical law

Symmetry

How do you use the calculator to find inequalities?

Normal cd

How can we use the calculator to find probabilities?

Inverse Normal

What are the key points to remember when drawing on the same axis?

Short and wide - more spread

Thin and tall - less spread

How do you find one paremter?

Find the z value and substitute into the equation z= x-mean /standard deviation

How do you find 2 parameters?

Use simultaneous equations to solve for mean and sd

What is the standard normal distribution?

Z ~ N (0,1)

What are the two types of modelling types and how do you recognise them?

1- use the Empirical law to look for something that doesn't fit

2- using a sample of data to compare proportions

What is the process of finding a probability using the normal approximation?

Using normal cd, typing in the Lowe and upper bounds, mean and standard deviation

What is the distribution of sample means a test for?

The population mean

What are the conditions for the distribution of sample means?

• Sample must be random

• Population must follow a normal distribution

What are the 6 steps to a sample means test

Step 1

H0: p= ⋯

H1: p < > ≠ ⋯

Step 2

X~N(standard deviation ²/n)

Step 3

The test statistic is the value for the mean of the sample

Step 4

Critical values are found:

• Using the distribution X~N(standard deviation ²/n)

, the mean is ALWAYS the one in H0

• Inverse normal function on your calculator

Two tail test ⇒ SPLIT the significance level and find both critical regions

Lower tail: Area = significance level

Upper tail: Area = 1 – significance level

Step 5

Compare and Reject/Do Not Reject H0

Step 6

Conclusion and context “population mean”