Let x be a binomial random variable with n = 20 and p = .1. a. Calculate

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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 MINITAB output at the top of the page 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?

MINITAB Output for Exercise 5.19 Probability Density Function Binomial with n = 20 and p = 0.1 P( X = x ) 0.121577 0.270

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Introduction To Probability And Statistics

ISBN: 9780495389538

13th Edition

Authors: William Mendenhall, Robert J. Beaver, Barbara M. Beaver

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