Let x be a binomial random variable with n = 20 and p = .1.
a. Calculate P(x ‰¤ 4) using the binomial formula.
b. Calculate P(x ‰¤ 4) using Table 1 in Appendix I.
c. Use the Excel output below 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 µ ± σ, µ ± 2σ and µ ± 3σ. 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?
Binomial with n = 20 and p = .1

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p(x) p(x) 7E-07 5E-08 4E-09 2E-10 9E-12 3E-13 8E-15 2E-16 2E-18 1E-20 0.1216 1 0.2702 2 0.2852 12 13 14 15 16 17 18 19 20 0.1901 4 0.0898 5 0.0319 6 0.0089 7 0.0020 8 0.0004 9 10 0.0001 0.0000