What is another name for a smooth curve (normal distribution)
A probability density function (pdf)
What conditions are required for a normal curve to be a PDF?
1) P(x) >= 0 for all X (no outcomes can have a probability of 0)
2) The area under the curve is equal to 1
What kind of variable is related to a probability density function?
A continuous random variable
What is a Z-score?
The distance of a piece of data from the mean in terms of standard deviation
What is the purpose of the Z-table?
Shows the different probabilities of events in regards to Z-scores
What is the general method for finding probabilities with Z-scores?
When Z is positive, add the corresponding probability to 0.5.
When Z is negative subtract the corresponding probability from 0.5.
What does a Z-score of 1 mean? (in terms of pdf)
Distance of ONE STANDARD DEVIATION from the center (recall that 1 SD = 68% of data for normally distributed data)
REVIEW: What are the percentages of data corresponding to different levels of standard deviation? (1σ vs 2σ vs 3σ)
1σ = 68% of data
2σ = 95% of data
3σ = 99.7 % of data
When is the continuity correction used?
Only when n is very larges
What are the conditions of the Continuity Correction?
1) np >= 5 and nq >= 5 then X (binomial distribution) can be considered a normal distribution.
2) The approximation works best when np >= 10 and nq >= 10
How do you decide whether to add or subtract 0.5 in the Continuity Correction?
It depends if you want to include or exclude a.
Decide depending on the case.
How to convert a Binomial to a Normal distribution?
(STEPS)
1) Solve for basic values (np, q, nq)
2) Solve for standard deviation (σ = (npq)^-1/2)
3) SHOW APPROXIMATION:
X~B(x; MEAN, STANDARD DEVIATION) = Y~N(MEAN, STANDARD DEVIATION)
* Values for Binomial are usually given, values of Normal are calculated*
How to fill in Binomial / Normal distribution equations?
B(x; n, p) VALUES GIVEN
N(x; np, σ) VALUES CALCULATED
