Question

Styles First we will learn how to evaluate binomial distribution with the help of Excel. Let's flip a coin n times and count how many tails we are going to get. If n=0, then no coin is tossed and the only option is 0 tails. Therefore P(0)=1, the mean is 0 and the standard deviation is 0. We are going to do a simple table for n=0. First we will define columns. Click on cell A1 and type X for our variable. Click on enter. Then click on B1 and input p(x) for probability. Click on cell A2 and type 0. Click on enter. Click on cell B2 and type 1. That completes the table. Now let's also evaluate mean and standard deviation. Click on cell D1 and type mean. Click on cell E1 and type variance. Click on cell F1 and type SD. Let's put in the formulas. Click on cell D2 and type=a2*b2. Click on cell E2 and type =b2*(a2-d2)^2. Click on cell F2 and type =sqrt(e2). We will indicate that we have a binomial distribution by clicking on H1 and typing in n, then we'll go to H2 and type 0. We'll go to 11 and type p and then we'll go to 12 and type=1/2. Now we will do n=1. First we will define columns. Click on cell A4 and type X for our variable. Then click on B4 and input p(x) for probability. Click on cell 04 and type mean.. Click on cell E4 and type variance. Click on cell F4 and type SD. When n=1 the only two options are 0 tails and 1 tail. Thus, we click on cell A5 and type 0 and we click on cell A6 and type 1. Let's now use binomial formula to evaluate probabilities. Click on cell B5 and type=BINOMDIST(0,1,1/2,FALSE). Click on enter. In this formula for binomial distribution there are four parameters, the first means we are looking for the probability of getting 1 tail. The second means we are flipping 1 coin. The third means that the probability of getting a tail in a flip is %. The last parameter False says that we are not looking into cumulative probability. We may use True instead when we are looking for the median for example, but that is not the topic here. Now that we learned that, we will evaluate probability of getting 1 coin. Click D. Focus

Answer 1

Sol:

Exercise 1.

Make the binomial probability distribution table for n=4 and p=1/2.

	4	n
	0.5	p
		cumulative
X	P(X)	probability
0	0.06250	0.06250
1	0.25000	0.31250
2	0.37500	0.68750
3	0.25000	0.93750
4	0.06250	1.00000
	1.00000
	2.000	expected value
	1.000	variance
	1.000	standard deviation

Exercise 2.

Make the binomial probability distribution table for n=5 and p=1/2.

	5	n
	0.5	p
		cumulative
X	P(X)	probability
0	0.03125	0.03125
1	0.15625	0.18750
2	0.31250	0.50000
3	0.31250	0.81250
4	0.15625	0.96875
5	0.03125	1.00000
	1.00000
	2.500	expected value
	1.250	variance
	1.118	standard deviation

Exercise 3.

Make the binomial probability distribution table for n=6 and p=1/3.

	6	n
	0.3333	p
		cumulative
X	P(X)	probability
0	0.08779	0.08779
1	0.26337	0.35117
2	0.32922	0.68038
3	0.21948	0.89986
4	0.08230	0.98217
5	0.01646	0.99863
6	0.00137	1.00000
	1.00000
	2.000	expected value
	1.333	variance
	1.155	standard deviation

Exercise 4.

Make the binomial probability distribution table for n=8 and p=1/3.

	8	n
	0.3333	p
		cumulative
X	P(X)	probability
0	0.03902	0.03902
1	0.15607	0.19509
2	0.27313	0.46822
3	0.27313	0.74135
4	0.17071	0.91206
5	0.06828	0.98034
6	0.01707	0.99741
7	0.00244	0.99985
8	0.00015	1.00000
	1.00000
	2.667	expected value
	1.778	variance
	1.333	standard deviation

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