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Construct and Interpret Binomial Distributions

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Learn about binomial distributions, random variables, and probability distributions. Calculate probabilities and identify discrete vs continuous variables. Solve problems with binomial experiments. Vocabulary from statistics textbook.

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Construct and Interpret Binomial Distributions

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  1. Construct and Interpret Binomial Distributions

  2. Combinations nCk • How many different committees of 4 students can be chosen from a group of 15?

  3. Vocabulary Page 212 book 238 NTG • A random variable is a variable whose value is determined by the outcomes of a random event. • A discrete random variable is a variable that can take on only a countable number of distinct values. • A continuous random variable is a variable that can take on an uncountable, infinite number of possible values, often over a specified interval.

  4. More Vocabulary • A probability distribution is a function that gives the probability of each possible value of a random variable. The sum of all the probabilities in a probability distribution must equal 1. • A binomial distribution shows the probabilities of the outcomes of a binomial experiment.

  5. A Binomial Experiment • A binomial experiment has n independent trials, with two possible outcomes (success or failure) for each trial. The probability for success is the same for each trial. The probability of exactly k successes in n trials is

  6. Symmetric/Skewed • A probability distribution is symmetric if a vertical line can be drawn to divide the histogram of the distribution into two parts that are mirror images. • A distribution that is not symmetric is called skewed.

  7. Sum of a Pair of 4 sided die

  8. = 16

  9. NTG Page 240 Independent Success Failure Same

  10. HW NTG page 243 #1 – 17

  11. binomcdf 20 trials: p: x value: Paste • This is n • Probability • X value in which you are interested. Leave this empty if you want all “n” values • Paste places command on the home screen 0.25 binomcdf(20, 0.25 STO --> L2

  12. binompdf or binomcdf

  13. binompdf binomcdf binompdf(5, 0.1 binomcdf(5, 0.1

  14. Textbook Page 215#1, 2, 5 – 16 Decide whether the random variable X is discrete or continuous. Explain. • X represents the amount of time it takes to brush your teeth. • X represents the number of days with a low temperature below freezing in January.

  15. Calculate the probability of tossing a coin 25 times and getting the givennumber of heads. 5. 2 6. 10 7. 18 8. 25

  16. Calculate the probability of k successes for a binomial experiment consisting of n trials with probability p of success on each trial.

  17. Match the values of n and p for a binomial distribution with the histogram that shows the probability of exactly k successes.

  18. #16 Turn this in by Tuesday

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