Wednesday, October 8, 2008 Lab Two- 1 Mr. PhillipsBinomial Distribution: Excel:2007This lab uses the binomial distribution as a descriptive tool to show the shape of the distribution as it varies with different parameters.I. In Roman numeral one, we examine the case of a fair coin and flipping it various times, i.e. a sequence of Bernoulli trials, where the number of trials varies.A. In cell C3, type one flip of a fair coin. In cell C5 type n, the number of trials and in C6 and C7 type 1. In cell D5 type k the number of heads or successes and in cell D6 type 0 and in Cell D7 type 1. In cell E5 type p for probability and in cell E6 typean equal sign =, and choose binomdist. For number_s, select cell D6. For trials, select cell C6, for probability type in 0.5, and for cumulative type in false to get the density function. Hit OK and drag from E6 through E7.B. To illustrate the distribution, select D6 through E7 and insert (heading or menu next to home) a scatter diagram. If necessary switch row and column ( below insert heading). Select the layout heading and put a chart title above the graph and type One Flip of a Fair Coin. Select legend and choose None. Select axis titles and for the horizontal axis type Number of Successes. For the vertical title type probability. Select the chart by clicking on it and choose the design heading or menu and select change chart type and choose column. You can change column width by right clicking on a column and choose format data point and moving gap width towards no gap. With the chart and design menu selected, choose move chart and move to a separate sheet.C. Replicate for two flips , three flips, ten flips, and twenty flips. Note how the distribution becomes more continuous as it stays symmetric.II. In Roman numeral two, we conduct a similar exercise but for an asymmetric Bernoulli trial such as throwing a fair die, where a six is a success and not a six is not a success. As the number of trials increases, this asymmetric Bernoulli trial yields a Binomial distribution that becomes more symmetric.A. Select Sheet two. In cell C3, type one flip of a fair die. In cell C5 type n, the number of trials and in C6 and C7 type 1. In cell D5 type k the number of heads or successes and in cell D6 type 0 and in Cell D7 type 1. In cell E5 type p for probability and in cell E6 type an equal sign =, and choose binomdist. For number_s, select cell D6. For trials, select cell C6, for probability type in 1/6, and for cumulative type in false to get the density function. Hit OK and drag from E6 through E7.Wednesday, October 8, 2008 Lab Two- 2 Mr. PhillipsBinomial Distribution: Excel:2007B. For the graphics, go through the steps as in IB, above.C. Replicate for two trials, ten trials , and thirty trials.III. In Roman numeral three we explore the normal distribution as an approximation to the binomial distribution. This is a good approximation for np>=5 and n(1-p)>=5. Using our fair die as an example, p=1/6 and n=30 meets these requirements. The normal distribution is described by two parameters, the mean and the standard deviation. The mean of the binomial is np = 30*(1/6) =5 and th variance of the binomial is n*p*(1-p) = 30*(1/6)*(5/6) = 25/6. The square root of the variance is the standard deviation and this is 2.041.A. First we compare the binomial distribution for thirty tosses of a fair die with the normal with the same mean and variance. Select Sheet three. In cell C3, type thirty tosses of a fair die. In cell C5 type n, the number of trials and in C6 and C7 type 30 and drag down through c36. In cell D5 type k the number of heads or successes and in cell D6 type 0 and in Cell D7 type 1 and drag down through D36.In cell E5 type binomial and in cell E6 type an equal sign =, and choose binomdist. For number_s, select cell D6. For trials, select cell C6, for probability type in 1/6, and for cumulative type in false to get the density function. Hit OK and drag from E6 through E36. In F5 type normal and in F6 type an +, and choosenormdist. For x select cell D6. For mean type in 5. For standard_dev type in 2.041, and for cumulative type false and hit OK, and drag down to F36.B. For the graphics, select D5 through F36 and the Insert menu and scatter diagram.Since the binomial is a discrete distribution, on the chart select as blue diamond and then select column chart.to get the continuous normal distribution plotted against the discrete binomial distribution.C. Replicate, but instead of the normal use the normal with a continuity correction .ie.a mean of 5.5.P(a k b) P[(a – ½ - np)/)1( pnp z [(b + ½ - np)/)1( pnp ]Wednesday, October 8, 2008 Lab Two- 3 Mr. PhillipsBinomial Distribution:
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