Computing Binomial Probabilities With Minitab

6
 Computing binomial probabilities with Minitab  You can compute binomial probabilities with Minitab in the following way. Suppose you have a binomial distribution with 15 trials (n=15) and probability of success p=0.7. In the following you will see how to compute probabilities of exact events and cumulative probabilities with Minitab. For example to compute the probability of exactly 5 successes you go to: CALC- and choose Probability Distributions  Binomial in the drop menu. Press OK. Choose “probability” in the window that opens, then type in the number of trials (n, so 15 in this case) and the probability of success p (i.e. 0.7) in the “ event probability” box.  You may have the value for the number of successes inserted in a column in which case you refer to it in the “ input column” box, or you can type the value in the “input constant” box. Press OK. (see screen shot on next page) The result will appear in the session window in Minitab. Here is the session output: Probability Density Function Bi nom i al w i t h n = 15 and p = 0. 7 x P( X = x ) 5 0. 002 980 3

description

COMP

Transcript of Computing Binomial Probabilities With Minitab

  • Computing binomial probabilities with Minitab

    You can compute binomial probabilities with Minitab in the following way. Suppose you have a binomial distribution with 15 trials (n=15) and probability of success p=0.7. In the following you will see how to compute probabilities of exact events and cumulative probabilities with Minitab. For example to compute the probability of exactly 5 successes you go to: CALC-and choose Probability Distributions Binomial in the drop menu. Press OK.

    Choose probability in the window that opens, then type in the number of trials (n, so 15 in this case) and the probability of success p (i.e. 0.7) in the event probability box. You may have the value for the number of successes inserted in a column in which case you refer to it in the input column box, or you can type the value in the input constant box. Press OK. (see screen shot on next page) The result will appear in the session window in Minitab. Here is the session output: Probability Density Function Binomial with n = 15 and p = 0.7 x P( X = x ) 5 0.0029803

  • To compute cumulative probabilities, you check the cumulative probability box in the binomial distribution window. For example, the probability of at most 10 successes, is ( 10) 0.4845P X = .

  • You can also generate the entire table of probabilities with Minitab. Start by typing the values of the number of successes in a column, say C1. If you work with the same binomial model with 15 trials you will have to insert all values from 0 to 15. You can do this more efficiently by using CALC- Make Patterned Data Simple Set of Numbers.

    Fill in the boxes in the window as see in the next picture and press Ok.

  • So you are asking Minitab to enter all values from 0 to 15 in the column C1. You will see the values appear in column C1. Next you use the probability distributions command (as described above) to compute the probabilities associated with the values in column C1, only that instead of using input constant box you use Input Column and select C1. For storage specify a different column, say C2. Press Ok. You will see the probabilities appear in column C2 in your worksheet.

    Unfortunately Minitab cannot draw the histogram of the data if it is given in two columns out of which one contains the probabilities associated with the values in the first column (or at least I havent found that out yet). Surprisingly enough this can be done with TI83. One way of getting the histogram of a binomial distribution is to generate random data following the given model and construct a histogram of the data generated. Here are the steps to do just that. We will generate 1000 values from a Binomial model with 15 trials and probability p=0.7 of success. That is, Minitab will generate 100 rows of data that will represent the number of successes out of 15 trials. Choose CALC- Random Data Binomial. Enter the number of rows to generate (1000 in our case), specify the number of trials and the probability of success as well as the column where you want the data to be stored (C3 on our screen). Press OK. See screen shots on next page.

  • Then, using STAT Basic Statistics Display Descriptive Statistics you can perform the descriptive analysis of the data that was generated and you may add to it a graph (histogram of the data for example).