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6 Pages

### math 221 Week 4 lab

Course: MATH 221, Spring 2012
School: DeVry Manhattan
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Word Count: 856

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Lab Statistics Week 4 MATH221 Statistical Concepts: Probability Binomial Probability Distribution Calculating Binomial Probabilities Open a new MINITAB worksheet. We are interested in a binomial experiment with 10 trials. First, we will make the probability of a success . Use MINITAB to calculate the probabilities for this distribution. In column C1 enter the word success as the variable name (in the shaded...

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Lab Statistics Week 4 MATH221 Statistical Concepts: Probability Binomial Probability Distribution Calculating Binomial Probabilities Open a new MINITAB worksheet. We are interested in a binomial experiment with 10 trials. First, we will make the probability of a success . Use MINITAB to calculate the probabilities for this distribution. In column C1 enter the word success as the variable name (in the shaded cell above row 1. Now in that same column, enter the numbers zero through ten to represent all possibilities for the number of successes. These numbers will end up in rows 1 through 11 in that first column. In column C2 enter the words one fourth as the variable name. Pull up Calc > Probability Distributions > Binomial and select the radio button that corresponds to Probability. Enter 10 for the Number of trials: and enter 0.25 for the Event probability:. For the Input column: select success and for the Optional storage: select one fourth. Click the button OK and the probabilities will be displayed in the Worksheet. Now we will change the probability of a success to . In column C3 enter the words one half as the variable name. Use similar steps to that given above in order to calculate the probabilities for this column. The only difference is in Event probability: use 0.5. Finally, we will change the probability of a success to . In column C4 enter the words three fourths as the variable name. Again, use similar steps to that given above in order to calculate the probabilities for this column. The only difference is in Event probability: use 0.75. Plotting the Binomial Probabilities 1. Create plots for the three binomial distributions above. Select Graph > Scatter Plot and Simple then for graph 1 set Y equal to one fourth and X to success by clicking on the variable name and using the select button below the list of variables. 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 below. Sca t t e r pl ot of one f our t hv ssucce ss 0. 30 0. 25 o ne f ou r t h 0. 20 0. 15 0. 10 0. 05 0. 00 0 2 4 succe ss 6 8 10 8 10 Sca t t e r pl ot of t hr e e f our t hv ssucce ss 0. 30 0. 25 t hr e e f our t h 0. 20 0. 15 0. 10 0. 05 0. 00 0 2 4 succe ss 6 Sca t t e r pl ot of one ha l f v ssucce ss 0. 25 one ha lf 0. 20 0. 15 0. 10 0. 05 0. 00 0 2 4 succe ss 6 8 10 Calculating Descriptive Statistics Open the class survey results that were entered into the MINITAB worksheet. 2. Calculate descriptive statistics for the variable where students flipped a coin 10 times. Pull up Stat > Basic Statistics > Display Descriptive Statistics and set Variables: to the coin. The output will show up in your Session Type Window. the mean and the standard deviation here. Mean: 4.600 Standard deviation: 1.429 Short Answer Writing Assignment Both the calculated binomial probabilities and the descriptive statistics from the class database will be used to answer the following questions. 3. List the probability value for each possibility in the binomial experiment that was calculated in MINITAB with the probability of a success being . (Complete sentence not necessary) P(x=0) P(x=1) P(x=2) 0.0009766 0.0097656 0.0439453 P(x=6) P(x=7) P(x=8) 0.205078 0.117188 0.0439453 P(x=3) P(x=4) P(x=5) 0.117188 0.205078 0.246094 P(x=9) P(x=10) 0.0097656 0.0009766 4. Give the probability for the following based on the MINITAB calculations with the probability of a success being . (Complete sentence not necessary) P(x1) P(x>1) P(4<x 7) 5. 0.999023 0.989258 0.568359 P(x<0) none 0.376953 P(x4) P(x<4 or x7) 0.623047 Calculate the mean and standard deviation (by hand) for the MINITAB created binomial distribution with the probability of a success being . Either show work or explain how your answer was calculated. Mean = np, Standard Deviation = npq Mean: 5 Standard deviation: 1.5 6. Calculate the mean and standard deviation (by hand) for the MINITAB created binomial distribution with the probability of a success being and compare to the results from question 5. Mean = np, Standard Deviation = npq Mean: 2.5 Standard deviation: 1.4 Comparison: Mean has been reduced to the half of that in question 5. Standard 7. Calculate the mean and standard deviation (by hand) for the MINITAB created binomial distribution with the probability of a success being and compare to the results from question 6. Mean = np, Standard Deviation = npq Mean = np = 10 * = 7.5 Standard deviation = 3 3 np ( 1 p ) = 10 * 1 = 1.4 4 4 8. Explain why the coin variable from the class survey represents a binomial distribution. 1. There are a fixed number of trials of 10. There are n trials. 2. Each trial results in either head or tail. That is, each trial has two possible outcomes, success or failure. 3. The probability of success is the same for each trial. 4. Each trial is independent. That is, the experiment satisfies all the conditions of a binomial experiment. Hence it is a binomial experiment. 9. Give the mean and standard deviation for the coin variable and compare these to the mean and standard deviation for the binomial distribution that was calculated in question 5. Explain how they are related. Mean = np, Standard Deviation = npq Mean & standard deviation for the coin variable Mean: 5.0 Standard deviation: 3.3 Mean & standard deviation for the binomial distribution Mean = np = 10 * = 5 Standard deviation = 1 1 np ( 1 p ) = 10 * 1 = 1.6 2 2 Mean is identical in both cases.
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