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Lecture Slides

Lecture Slides. Elementary Statistics Eleventh Edition and the Triola Statistics Series by Mario F. Triola. Chapter 5 Discrete Probability Distributions. 5-1 Review and Preview 5-2 Random Variables 5-3 Binomial Probability Distributions

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Lecture Slides

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  1. Lecture Slides Elementary StatisticsEleventh Edition and the Triola Statistics Series by Mario F. Triola

  2. Chapter 5DiscreteProbability Distributions 5-1 Review and Preview 5-2 Random Variables 5-3 Binomial Probability Distributions 5-4 Mean, Variance and Standard Deviation for the Binomial Distribution

  3. Section 5-4 Mean, Variance, and Standard Deviation for the Binomial Distribution

  4. Key Concept In this section we consider important characteristics of a binomial distribution including center, variation and distribution. That is, given a particular binomial probability distribution we can find its mean, variance and standard deviation. A strong emphasis is placed on interpreting and understanding those values.

  5. For Any Discrete Probability Distribution: Formulas Meanµ = [x•P(x)] Variance2= [x2•P(x) ] –µ2 Std. Dev = [x2•P(x) ] –µ2

  6. Binomial Distribution: Formulas Meanµ = n•p Variance2 = n•p•q Std. Dev. = n • p • q Where n = number of fixed trials p = probability of success in one of the n trials q = probability of failure in one of the n trials

  7. Interpretation of Results Maximum usual values = µ + 2 Minimum usual values = µ– 2  It is especially important to interpret results. The range rule of thumb suggests that values are unusual if they lie outside of these limits:

  8. Recap In this section we have discussed: • Mean, variance and standard deviation formulas for any discrete probability distribution. • Mean, variance and standard deviation formulas for the binomial probability distribution. • Interpreting results.

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