Statistics - Normal Flashcards
What is the normal distribution?
Continuous probability distribution
What is the area under the curve of the normal distribution?
1
What is the notation for a normal distribution?
X~N(μ,σ^2)
μ - mean
σ^2 - varience
σ - standard dev
What is the shape of the normal distribution?
Bell-shaped curve with asymptotes at each end
How is the normal distribution symmetrical?
Symmetrical about x = μ
mean = mode = median
Where are the points of inflection on the normal distribution?
μ + σ AND μ-σ
What is σ?
Standard deviation
What % of data lies within 1 standard deviation of mean?
Approx 68%
What % of data lies within 2 standard deviations of the mean?
Approx 95%
What % of data lies within 3 standard deviations of the mean?
Nearly all
What is the upper/lower when only one boundary given?
If lower boundary given, the upper is 5*σ + mean
If upper boundary given, the lower is mean - 5*σ
Why can you use >/< instead of >= / <= ?
No difference as its a continuous normal distribution
What is the standard normal distribution?
Normal distribution is when
μ = 0
σ = 1
How is the standard normal distribution shown?
Z~N(0,1^2)
What is the coding for standard normal distribution?
Z = (X-μ) / σ
What should be done if the probability to the right is given with a standard value (top %)?
Use percentage points table
When can you approx the normal from a binomial distribution?
n is large (above 50)
p is close to 0.5
How do you calculate μ & σ from binomial when approximating?
μ = np σ = √(np-n*p^2) = √(μ*(1-p))
What is continuity correction?
Probabilities are discrete in binomial
When approximating to normal you must correct to make it continuous
How do you continuity correct a variable that is less than or equal to 70?
Use values less than 70.5
What is the sample mean of a sample size n taken from a normally distributed sample X?
x̄~N(μ, σ^2/2)
What is the Z value when coding a sample mean?
Z = X-μ/ (σ/√n)
