This document contains all of the key information for binomial distributions and normal distributions (with inverse and standard normal), and then explains the process of hypothesis testing (+ how to apply it to binomial distributions, normal distributions and the product moment correlation coeffic...
Binomial Distributions
The Binomial Probability Function
P (r successes in n trials) = nCr x pr x (p-1)n-r
Conditions for a Binomial Distribution
1. All trials are independent
2. The probability of success is the same in each trial
3. There is a fixed number of trials
4. Each result is either a ‘success’ or ‘failure’
5. The variable is the total number of successes in the trials
The Binomial Distribution
If the above conditions are satisfied then P (X = x) = nCx x px x (1-p)n-x, which can be written as X ~ B (n,p)
• The expected number of successes is given by n x p
• Use the ‘probability distribution function’ on the calculator to find P (X = x)
• Use the ‘cumulative distribution function’ on the calculator to find P (X ≤ x)
o P (X < x) = P (X ≤ x-1)
o P (X > x) = 1 - P (X ≤ x)
o P (X ≥ x) = 1 - P (X ≤ x-1)
Normal Distributions
The Normal Distribution
If X is normally distributed with mean µ and variance σ2, it is written as X ~ N (µ,σ2)
• Approx. 2/3 of the data lie within one standard
deviation of the mean
• Approx. 95% of the data lies within two
standard deviations of the mean
• Approx. 99.7% of the data lies within three
standard deviations of the mean
• There are points of inflection at x = µ ± σ
• The probability of the random variable taking a value between 2 limits is the area under the graph
between those limits
• The graph is symmetrical, so values the same distance above and below the mean are equal
• For a continuous variable, P (X ≤ k) = P (X < k)
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller JunaidAli025. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for £0.00. You're not tied to anything after your purchase.