Question: 33. Let x be a binomial random variable with n520 and p5.1. a. Calculate P(x#4) using the binomial formula. b. Calculate P(x#4) using Table 1

33. Let x be a binomial random variable with n520 and p5.1.

a. Calculate P(x#4) using the binomial formula.

b. Calculate P(x#4) using Table 1 in Appendix I.

c. Use the following Excel output to calculate P(x#4).

Compare the results of parts

a, b, and c.

d. Calculate the mean and standard deviation of the random variable x.

e. Use the results of part d to calculate the intervals m 6s, m 62s, and m 63s. Find the probability that an observation will fall into each of these intervals.

f. Are the results of part e consistent with Tchebysheff’s Theorem? With the Empirical Rule?

Why or why not?

Excel output for Exercise 33: Binomial with n = 20 and p

Excel output for Exercise 33: Binomial with n = 20 and p = .1 A B C D 1 x p(x) p(x) 234 2 0 0.1216 11 7E-07 1 0.2702 12 5E-08 4 2 0.2852 13 4E-09 5. 3 0.1901 14 2E-10 6 4 0.0898 15 9E-12 7 5 0.0319 16 3E-13 8 6 0.0089 17 8E-15 9 7 0.0020 18 2E-16 10 8 0.0004 19 2E-18 11 9 0.0001 20 1E-20 12 10 0.0000

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