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Understanding Mean and Standard Deviation in Probability Distributions

This chapter focuses on calculating the mean and standard deviation of probability distributions using statistical calculators. Step-by-step instructions are provided for inputting values and running calculations for both generic distributions and binomial distributions. Additionally, it discusses whether specific procedures result in binomial distributions, using coin flips and die rolls as examples. An included packet addresses various statistical problems, enhancing understanding and application of concepts. Prepare for collaborative review sessions and deepen your grasp of probability and statistics.

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Understanding Mean and Standard Deviation in Probability Distributions

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  1. Chapter 5 review

  2. Mean and Standard deviation of a probability distribution • On calculator: Enter in the possible values for random variable in L1, and the probability of each value in the corresponding L2 spot. • Click STATS  CALC  1-Var Stats  L1, L2

  3. Calculate the mean and standard deviation

  4. Binomial Distributions • P(x) • On calculator: 2nd + VARS  Binompdf  (n, p, X) • Table is also option n: number of trials p: probability of success q: probability of failure x: number of successes desired

  5. Example • Given the following information determine the mean, standard deviation, and probability of x successes for the binomial. • n= 12, x=5, p=.5

  6. Critical Question • Does the following procedure result in a binomial distribution? • Flipping a coin 30 times and counting the number of heads • Rolling a die 43 times and keeping track of the number of 6’s • Rolling a die 25 times and keeping track of what number is rolled

  7. Packet time • Finish working on your packet • We will go over the packet answers at the end of class. • Good luck studying tonight!!!

  8. Packet Answers • 1. Statistic • 2 – a. Discrete • 2 – b. Continuous • 3 – a. Ratio • 3 – b. Interval • 4 – a. Cluster • 4 – b. Systematic • 4 – c. Stratified • 5 – a. 26% • 5 – b. 95% • 5 – c. x=80 • 5 – d. 4 clients • 6 – a. Possible, but unlikely • 6 – b. Possible and likely. • 7. 3 • 8. 10 • 9. 14.5 and 17.5 • 10. 6 • 11-12 (See Buda’s Packet) • 13 – a. 12,529 • 13 – b. 5, 159 • 14. 54.79 • 15. 57.43 • 16. 104.83% • 17 – a. z=-0.75 • 17 – b. z = 0.80

  9. Packet Answers Continued • 18 – a. 12 • 18 – b. 57 • 19. 71th percentile • 20. No outliers • 21. 0 and 1 • 22 – a. Not disjoint. • 22 – b. Disjoint. • 23 – a. 0.857 • 23 – b. 0.815 • 23 – c. 0.915 • 24 – a. 0.013 • 24 – b. 0.201 • 25 – a. 0.000129 • 25 – b. 0.006 • 26 – a. 0.570 • 26 – b. 0.560 • 27 – a. {NNN, NNR} • 27 – b. {BW, WB, WW} • 28 – a. 0.999 • 28 – b. 0.512 • 29 – a. 0.006 • 29 – b. 0.054 • 29 – c. 0.103 • 30 – a. Not binomial • 30 – b. Binomial • 30 – c. Binomial

  10. Packet Answers - Continued • 31. 9.66 • 32 – a. 8.8 • 32 – b. 930.24 • 32 – c. 1746.36 • 33 – a. 3.02 • 33 – b. 22.46 • 33 – c. 3.36 • 34 – a. 0.007 • 34 – b. 0.212 • 34 – c. 0.122 • 35. Not enough info. • 36. The number of dogs families own. • 37. The three customers. • 38. The entire ice-cream parlor customer base. • 39. 0.100 • 40. 0.100 • 41. 0.400 • 42. 0.200 • 43. 0.200 • 44. 68% of all values. • 45. Mean and midrange

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