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Understanding Binomial Distribution: Mean & Standard Deviation Calculation

This guide covers the fundamentals of binomial distribution, including how to calculate the mean and standard deviation for binomial experiments following the BINS criteria: Binary outcomes, Independent trials, Fixed number of trials, and Constant probability of success. Through practical examples, such as calculating probabilities for shopping behaviors and patient survival rates, you will learn to apply the binomial formula effectively. Homework worksheets are included for practice. Perfect for students seeking to understand probability distributions!

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Understanding Binomial Distribution: Mean & Standard Deviation Calculation

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  1. Find the mean & St. Dev for each.

  2. Find the mean & standard deviation

  3. Binomial Distribution formula Section 6.3A

  4. Binomial Experiment - BINS • Binary? • There are two possible outcomes – success and failure • Independent? • Trials must be independent • Number? • The number of trials must be fixed – out of n…. • Success? • On each trial the probability of success must be the same

  5. Let E be the event that a person goes out shopping on Black Friday. Find the probability distribution for a sample of 3 people if the P(E) = .78.

  6. Probability distribution of going shopping on black Friday for 4 people. P(E) = .78

  7. Let’s Develop the formula! • If I have 5 people, how many ways can I arrange them? • How many ways can I choose 2 of the 5 who went shopping on black Friday? • But every set of two is the same (SSNNN = SSNNN)…

  8. Binomial Distribution where

  9. The survival rate for a risky operation is 80%. What is the probability that exactly 4 of the next 5 patients survive?

  10. USA today stated that 45% of Americans know somebody who became addicted to a drug other than alcohol. If we randomly ask 15 people, what’s the probability that exactly 3 were addicted?

  11. What’s the probability that at least 12 are addicted?

  12. What the probability that less than 3 are addicted?

  13. 90% of the trees planted by a landscaper will survive. If 10 trees are planted, what’s the probability more than eight survive?

  14. The probability that a person will subscribe to Statistics Monthly is 48%. Find the probability that out of a group of seven, at least one person subscribes.

  15. There are charts as well – but only for some probabilities so you need to know the formula.

  16. Homework • Worksheet

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