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(solution) 1. Some tables for the binomial distribution give values only up


1. Some tables for the binomial distribution give values only up to 0.5 for the probability of success p. There is a symmetry between values of p greater than 0.5 and values of p less than 0.5.

(a) Consider the binomial distribution with n=10andp=.75. Since there are anywhere from 0 to 10 successes possible, put the numbers 0 through 10 in Cells A2 through A12. Use Cell A1 for the label r. Use BINOM.DIST with cumulative False option to generate the probabilities for r = 0 through 10.

Store the results in Cells B2 through B12. Use Cell B1 for the label p = 0.75.

(b)  Now consider the binomial distribution with n = 10 and p = .25. Use BINOM.DIST with cumulative False option to generate the probabilities for r = 0 through 10. Store the results in Cells C2 through C12. Use Cell C1 for the label p = 0.25.

(c)  Now compare the entries in Columns B and C. How does P(r = 4 successes with p = .75) compare to P(r = 6 successes with p = .25)?

2. (a)  Consider a binomial distribution with fifteen trials and probability of success on a single trial p= 0.25. Create a worksheet showing values of r and corresponding binomial probabilities. Generate a bar graph of the distribution.

(b)  Consider a binomial distribution with fifteen trials and probability of success on a single trial p= 0.75. Create a worksheet showing values of r and the corresponding binomial probabilities. Generate a bar graph.

(c)  Compare the graphs of parts (a)and(b).How are they skewed?Is one symmetric with the other?


 


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