et x be a binomial random variable with n = 20 and p = 28 / 100. a-)Calculate the mean, variance and standard deviation of the random variable x.  b-)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. c- Are the results of part e consistent with Tch

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Let x be a binomial random variable with n = 20 and p = 28 / 100.

a-)Calculate the mean, variance and standard deviation of the random variable x.
 b-)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.
c- Are the results of part e consistent with Tchebysheff’s Theorem? With the Empirical Rule? Why or why not?

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