Stats, the normal distribution Flashcards
(15 cards)
What are identifying characteristics of the normal distribution?
Continuous p(x=a) = 0
Symmetrical around the mean
The area under the curve is 1
Asymptotes of the x axis
How much data must lay within 3 standard deviations of the mean?
99.7%
Why is is it that where X~N, P(X = a) = 0?
Since normal distributions are continuous there are an infinite amount of numbers between each value so the probability that x is equal too precisely one discrete value is infinitesimally small.
When modelling a Z score, what is the mean and standard deviation?
mean = 0, standard deviation = 1
What actually is a Z score?
The number of standard deviations that a test statistic sits from the population mean
How do we calculate the Z score?
X - μ / σ
How can you solve any distributions probability where P(x>a | x<b)?
Use P(A|B) = P(AnB) / P(B)
What is positive skew?
Data is heavy on the left graphically
What is negative skew?
Data is heavy on the right graphically
What are the conditions for modelling a binomial distribution as a normal one?
where X~B(n,p)
n must be large
p approximately = 0.5
Given X~B(n,p), what is the equivalent normal distribution?
X~N(np, np(1-p))
For a distribution of a sample taken from a normal population, what is the mean and the standard deviation?
The standard error = σ / √n
populations mean = sample mean
What is the adapted formula for the Z score of a sample (use standard error)?
Z sample = x̄ - μ / ( σ / √n)
What is the significance level (sample means hypothesis testing)?
The probability of rejecting H0 when H0 is infact true
How do you identify the critical test statistic of a normally distributed sample?
P (Z < critZ) = significance level
Inverse Z distribution
ϕ⁻¹ (sig level) = x̄ - μ / ( σ / √n)
