Central Limit Theorem
-as you take larger samples and find their averages, those averages form a normal (bell-shaped) curve — even if the original data wasn’t normal
-μX = the mean of X
- σX = the standard deviation of X
-n = how many values are in each sample (not how many samples you take).
normal distribution (the sampling distribution)
sample means from xbar
Standard Error of the mean
-standard deviation of x̄ (called the standard error) = σ / √n
X = one value
x̄ = an average from a sample
Both have the same overall mean (μ), but x̄’s spread (σ / √n) is smaller.
Central Limit Theorem for sums
The Central Limit Theorem for sums says:
If you keep taking bigger samples and add up their values, those sums will start to form a normal (bell-shaped) curve — even if the original data wasn’t normal.
-The mean of the sums = μ × n
-The standard deviation of the sums = σ × √n
xbar means
sample mean
to find the probability you may need to find what first
We find the standard deviation of the sample mean first because it shows how much sample averages vary — and that’s what the z-score and probability are based on.
formula when to find standard devations above the expected value and for sum
xbar=μ+z(σxbar)
-S=μS+z⋅σS
is n is larger than 30 usually it means
n is large and and the dist/mean is normal
what is the Ex in z = (ΣX – nμₓ) / (√n × σₓ)
the sum its looking for eg 7500
go over slide `
17
if the z score goes past 4 what is it
0
probability for expo CDF
P(X>x)=e ^−x/μ
