Statistics for Decision Making

1. Create plots for the three binomial distributions above create the scatter plots in Excel by selecting the data you want plotted and then click on INSERT, CHARTS, SCATTER, and then select the first chart shown which is dots with no connecting lines. Do this two more times and for graph 2 set Y equal to ‘one half’ and X to ‘success’, and for graph 3 set Y equal to ‘three fourths’ and X to ‘success’. Paste those three scatter plots in the grey area below. (9 points) 3. List the probability value for each possibility in the binomial experiment calculated at the beginning of this lab, which was calculated with the probability of a success being ½. (Complete sentence not necessary; round your answers to three decimal places) (8 points) P(x=0) 0.001 P(x=6) 0.205 P(x=1) 0.010 P(x=7) 0.117 P(x=2) 0.044 P(x=8) 0.044 P(x=3) 0.117 P(x=9) 0.010 P(x=4) 0.205 P(x=10) 0.001 P(x=5) 0.246 4. Give the probability for the following based on the calculations in question 3 above, with the probability of a success being ½. (Complete sentence not necessary; round your answers to three decimal places) (8 points) P(x≥1) 0.999 P(x<0) 0 P(x>1) 0.989 P(x≤4) 0.377 P(4<x ≤7) 0.568 P(x<4 or x≥7) 0.344 5. Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ½ and n = 10. Either show work or explain how your answer was calculated. Use these formulas to do the hand calculations: Mean = np, Standard Deviation = (4 points) Mean = np: 5 Standard Deviation = : 1.581 6. Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ¼ and n = 10. Write a comparison of these statistics to those from question 5 in a short paragraph of several complete sentences. Use these formulas to do the hand calculations: Mean = np, Standard Deviation = (4 points) Mean = np: 2.5 Standard Deviation = :1.369 Comparison: My mean was 2.5 compared to the mean of 5 I got in problem 5. That makes sense since the probability for this one is ¼. I would expect to get the results ¼ of the time. 7. Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ¾ and n = 10. Write a comparison of these statistics to those from question 6 in a short paragraph of several complete sentences. Use these formulas to do the hand calculations: Mean = np, Standard Deviation = (4 points) Mean = np: 7.5 Standard Deviation = :1.369 Comparison: My men was 7.5 compared to the mean of 5. That makes sense since the probability for this one is ¾. I would expect to get the results ¾ of the time 8. Using all four of the properties of a Binomial experiment (see page 201 in the textbook) explain in a short paragraph of several complete sentences why the Coin variable from the class survey represents a binomial distribution from a binomial experiment. (4 points) In order to explain the meaning and utility of distributions, it is necessary to first introduce the topic of random variables. The term random in Random Variable refers to the idea that each individual outcome has an equal chance of occurring. Therefore, each outcome is random determined. For example, a fair coin has an equal probability of flipping up heads as it does flipping up tails. Hance, the random variable is determined by the outcome of flipping a coin. 9. Compare the mean and standard deviation for the Coin variable (question 2) with those of the mean and standard deviation for the binomial distribution that was calculated by hand in question 5. Explain how they are related in a short paragraph of several complete sentences. (4 points) Mean from question #2: 4.400 Standard deviation from question #2: 1.499 Mean from question #5: 5 Standard deviation from question #5: 1.581 Comparison and explanation: The values in problem 2 were calculated using actual data. The results in problem 5 there were calculated using mathematical formula based on n and p. I would expect the resulted from actual date to get closer to the formula results as I get more and more data.    

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