THe normal disitribution

Question 1

What is the normal disitrbution

Answer 1

The normal distribution is a bell-shaped curve, a continuous probability distribution approximating the distribution of many variables in nature.

Question 2

What does a normal distirbution mean about the mean/ median/ mode

Answer 2

If a variable has a normal distribution, its mean, median, and mode are all the same. The normal distribution is symmetric around its mean.

Question 3

How many individuals are within 1sd/ 2sd/ 3sd

Answer 3

1sd: 68.3%

1.96sd: 95%

3sd: 99.7%

Question 4

Standard normal disitrbution

Answer 4

A standard normal distribution is a normal distribution with mean of zero and standard deviation equal to one.

All normal distributions can be converted to the standard normal distribution by computing, for each measurement, the number of standard deviations from the mean: Z=Y−μ/σ, where Z is called the “standard normal deviate.”

By calculating the Z value of a value from the data you can work out the probaility of getting a value equal or greater than this value.

Question 5

Central limit theorum

Answer 5

According to the central limit theorem, the sum (or average) of a large number of observations randomly sampled from a non-normal distribution is approximately normally distributed.

The sampling distribution of a non normal population will be normal if the sample size is large

Question 6

approximating binomial disitrbution by a normal disitrbution

Answer 6

A binomial distribution with large n can be approximated by a normal distribution.

As a rule of thumb, np (means) and n(1−p) (SD) should both be greater than five to use the normal approximation.

Question 7

Z standardisation test

Answer 7

The Z standardisation equation generates a Z values. The Z value is how many sd the data is from the mean. Using a statistical table, this Z value tell you the probability to getting a sample mean of this value or more extreme by assessing the Z value within a disitrbution.
Z= X bar (sample mean) - u (population mean)/ sigma (population standard deviation)/ sqrt sample size

This method requires you to know the population standard deviation.

If the population standard deviation is not known you can carry out a one sample T test using sample standard deviation instead.