MATH399 Statistics Week 4 Lab Name: _______________________ Statistical Concepts: Probability Binomial Probability Distribution Calculating Binomial Probabilities Open a new Excel worksheet. 1. 2. 3. 4. 5. Open spreadsheet In cell A1 type \"success\" as the label Under that in column A, type 0 through 10 (these will be in rows 2 through 12) In cell B1, type \"one fourth\" In cell B2, type \"=BINOM.DIST(A2,10,0.25,FALSE)\" [NOTE: if you have Excel 2007, then the formula is BINOMDIST without the period] 6. Then copy and paste this formula in cells B3 through B12 7. In cell C1, type \"one half\" 8. In cell C2, type \"=BINOM.DIST(A2,10,0.5,FALSE)\" 9. Copy and paste this formula in cells C3 through C12 10. In cell D1 type \"three fourths\" 11. In cell D2, type \"=BINOM.DIST(A2,10,0.75,FALSE)\" 12. Copy and paste this formula in cells D3 through D12 Plotting the Binomial Probabilities 1. Create plots for the three binomial distributions above. You can create the scatter plots in Excel by selecting the data you want plotted, clicking on INSERT, CHARTS, SCATTER, then selecting 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. (12 points) Version 20160311 Calculating Descriptive Statistics You will use the same class survey results that were entered into the Excel worksheet for the Week 2 iLab Assignment for question 2. 2. Calculate descriptive statistics for the variable (Coin) where each of the students flipped a coin 10 times. Round your answers to three decimal places and type the mean and the standard deviation in the grey area below. (4 points) Mean: Standard deviation: 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. Round all numeric answers to three decimal places. 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 . (Complete sentence not necessary; round your answers to three decimal places) (10 points) P(x=0) P(x=1) P(x=2) P(x=3) P(x=4) P(x=5) P(x=6) P(x=7) P(x=8) P(x=9) P(x=10) 4. Give the probability for the following based on the calculations in question 3 above, with the probability of a success being . (Complete sentence not necessary; round your answers to three decimal places) (12 points) P(x1) P(x>1) P(4B 21% E]- frameset.next.ecollege.com l Drlve (miles) State Sllue Slze Height (inches) Sleep (hours) Gender Car Color TV (hours) Money (dollars) Coin 33 SC 1 1 68 8 M blue 1 9.00 4 28 NY 7 67 4 F black I 29.00 4 77 PA 10 71 8 M blue 1 52.00 5 71 MI E 64 6 F blue 2 1.00 4 54 FL 9 70 S F green 2 5.00 3 31 CA 10 70 S F black 2 7.00 7 31} OR 10 67 8 F silver 2 15.00 4 29 TX 9 70 7 M silver 2 32.00 3 6 IL 12 63 7 F blue 2 44.00 2 78 CA 9 71 9 M blue 2 47,00 2 63 NY 1 l 67 S M green 3 4.00 6 36 MI 10 61 7 M blue 3 5.00 7 63 PA 10 66 8 F silver 3 5.00 7 36 TX 7 66 5 M mange 3 6.00 3 86 FL I l 69 8 M black 3 6.00 3 76 NY 9 65 7 F red 3 7.00 6 42 TX 9 73 7 F black 3 7.00 3 33 FL 13 69 8 M blue 3 8.00 3 j 20 IL 5 62 7 F black 3 10.00 2 94 KY 1 1 74 8 M red 3 20.00 4 39 SC 1 1 69 10 M red 3 26.00 4 88 CA 6 63 S F black 3 43.00 6 25 GA 9 69 7 M silver 3 53.00 5 80 NV 12 69 S M white 4 3.00 4 42 [L B 65 S F red 4 4.00 4 71 PA 7 74 8 M black 4 6.00 7 73 FL 12 70 7' F green 4 15,00 3 55 OH 9 67 S F dark blue 4 3 I .00 4 25 CA 8 69 6 F silver 4 34,00 4 76 PA 1] 7| 4 M silver 5 13.00 S I 40 IL 10 68 6 M green 5 16.00 S 4 NY 9 69 7 F blue 5 21,00 5 36 OR 9 73 7 M blue 5 23.00 5 I 54 CA 5 70 5 F green 6 6.00 7 6 OR 13 75 10 M silver 6 7.00 4 7.2 1.410047976 0613927301 Drive (miles) 33 28 77 71 54 81 38 29 6 78 63 36 63 36 86 76 42 83 20 94 39 88 25 80 42 71 73 55 25 76 40 4 36 54 6 State SC NY PA MI FL CA OR TX IL CA NY MI PA TX FL NY TX FL IL KY SC CA GA NV IL PA FL OH CA PA IL NY OR CA OR Shoe Size 11 7 10 8 9 10 10 9 12 9 11 10 10 7 11 9 9 13 5 11 11 6 9 12 8 7 12 9 8 11 10 9 9 5 13 Height (inches) 68 67 71 64 70 70 67 70 63 71 67 61 66 66 69 65 73 69 62 74 69 63 69 69 65 74 70 67 69 71 68 69 73 70 75 Sleep (hours) Gender Car Color 8 M blue 4 F black 8 M blue 6 F blue 8 F green 8 F black 8 F silver 7 M silver 7 F blue 9 M blue 8 M green 7 M blue 8 F silver 5 M orange 8 M black 7 F red 7 F black 8 M blue 7 F black 8 M red 10 M red 5 F black 7 M silver 8 M white 8 F red 8 M black 7 F green 8 F dark blue 6 F silver 4 M silver 6 M green 7 F blue 7 M blue 5 F green 10 M silver 7.2 1.4100479758 0.6139273013 TV (hours) 1 1 1 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 6 6 Money (dollars) 9.00 29.00 52.00 1.00 5.00 7.00 15.00 32.00 44.00 47.00 4.00 5.00 5.00 6.00 6.00 7.00 7.00 8.00 10.00 20.00 26.00 43.00 53.00 3.00 4.00 6.00 15.00 31.00 34.00 13.00 16.00 21.00 23.00 6.00 7.00 Coin 4 4 5 4 3 7 4 3 2 2 6 7 7 3 3 6 3 3 2 4 4 6 5 4 4 7 3 4 4 5 5 5 5 7 4 MATH399 Statistics Week 4 Lab Name: _______________________ Statistical Concepts: Probability Binomial Probability Distribution Calculating Binomial Probabilities Open a new Excel worksheet. 1. 2. 3. 4. 5. Open spreadsheet In cell A1 type \"success\" as the label Under that in column A, type 0 through 10 (these will be in rows 2 through 12) In cell B1, type \"one fourth\" In cell B2, type \"=BINOM.DIST(A2,10,0.25,FALSE)\" [NOTE: if you have Excel 2007, then the formula is BINOMDIST without the period] 6. Then copy and paste this formula in cells B3 through B12 7. In cell C1, type \"one half\" 8. In cell C2, type \"=BINOM.DIST(A2,10,0.5,FALSE)\" 9. Copy and paste this formula in cells C3 through C12 10. In cell D1 type \"three fourths\" 11. In cell D2, type \"=BINOM.DIST(A2,10,0.75,FALSE)\" 12. Copy and paste this formula in cells D3 through D12 Plotting the Binomial Probabilities 1. Create plots for the three binomial distributions above. You can create the scatter plots in Excel by selecting the data you want plotted, clicking on INSERT, CHARTS, SCATTER, then selecting 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. (12 points) Version 20160311 one fourth 0.3 0.25 0.2 Probability 0.15 0.1 0.05 0 0 2 4 6 8 10 12 8 10 12 Success one half 0.3 0.25 0.2 Probability 0.15 0.1 0.05 0 0 2 4 6 Success Version 20160311 three fourths 0.3 0.25 0.2 Probability 0.15 0.1 0.05 0 0 2 4 6 8 10 12 Success Calculating Descriptive Statistics You will use the same class survey results that were entered into the Excel worksheet for the Week 2 iLab Assignment for question 2. 2. Calculate descriptive statistics for the variable (Coin) where each of the students flipped a coin 10 times. Round your answers to three decimal places and type the mean and the standard deviation in the grey area below. (4 points) Mean: = 1/n xi=4.4 2 Standard deviation: = ( xix ) = 1 n1 1.499 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. Round all numeric answers to three decimal places. Version 20160311 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 . (Complete sentence not necessary; round your answers to three decimal places) (10 points) P(x=0) P(x=1) P(x=2) P(x=3) P(x=4) P(x=5) 0.001 0.010 0.044 0.117 0.205 0.246 P(x=6) P(x=7) P(x=8) P(x=9) P(x=10) 0.205 0.117 0.044 0.010 0.001 4. Give the probability for the following based on the calculations in question 3 above, with the probability of a success being . (Complete sentence not necessary; round your answers to three decimal places) (12 points) P(x1) P(x>1) P(41) 0.999 0.989 P(x<0) P(x4) 0 0.377 P(41) P(41) 0.999 0.989 P(x<0) P(x4) 0 0.377 P(4