Probability-binomial-distribution -1-v2 by ClassOf1

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									              Sub: Statistics                                                                            Topic: Probability



              Question:

              Probability values using binomial distribution.

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              Calculate each binomial probability:

              (a) Fewer than 7 successes in 15 trials with a 40 percent chance of success. (Round your
                  answer to 4 decimal places.)

                    Probability

              (b) At least 6 successes in 10 trials with a 70 percent chance of success. (Round your answer to
                  4 decimal places.)

                    Probability

              (c) At most 12 successes in 17 trials with a 90 percent chance of success. (Round your answer
                  to 4 decimal places.)

                    Probability

              (d) More than 13 successes in 19 trials with an 40 percent chance of success. (Round your
                  answer to 4 decimal places.)

                    Probability




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              Sub: Statistics                                                                            Topic: Probability

              Solution:


              (a) Fewer than 7 successes in 15 trials with a 40 percent chance of success. (Round your
                   answer to 4 decimal places.)
               The information can be represented in the following notation:


                                          Sample size: n = 15 trials
                                          Proportion: p=0.4
              Here X follows Binomial distribution with parameters n = 15 and p = 0.4

              The probability function of x is given by


                                                        n
                                          P[X = x] =        * p x * q n x , x = 0, 1, 2… n; and q = 1 – 0.4 = 0.6
                                                        x


                 Fewer than 7 successes


               X            NCx          P^x           q^(n-x)        P(X)
                        0         1         1           0.00047        0.00047
                        1        15       0.4          0.000784       0.004702
                        2       105      0.16          0.001306       0.021942
                        3       455    0.064           0.002177       0.063388
                        4      1365   0.0256           0.003628       0.126776
                        5      3003 0.01024            0.006047       0.18
								
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