Let r be a random variable representing the number of successes out of n trials. About 25% of people find an excuse (work, travel out of town, etc.) to avoid a call for a jury duty. If 8 people are called for a jury duty: a) What is the probability that 5 or more people will be available to serve on the jury? (7 points) b) Find the expected value and the standard deviation of those people that are available to serve on the jury. (8 points) Given information: Probability of success: Probability of failure: Number of trials: P = q= n = P(r 5) = ? Solution a) Find the probability that 5 or more people will be available to serve on the jury. r = The table below shows the P(r) values for n = 8. n 8 r 0 1 2 3 4 5 6 7 8 P(r 5) 0.01 0.05 0.10 .923 .663 .430 .075 .279 .383 .003 .051 .149 .000 .005 .033 .000 .000 .005 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 = *** Expected value = www *** *** *** *** *** 0.25 .100 .267 .311 .208 .188 .087 .023 .004 .000 n = P ... *** *** ... ... *** *** *** 0.55 p = .002 .016 .070 .172 .263 .257 .157 .055 b) Calculate the expected value and the standard deviation. Expected value: u = np .008 ... www ... *** ... www *** *** 0.75 .000 .001 .012 .058 .173 .311 .311 .133 .100 ... ... *** ... *** www ... 0.85 0.90 0.95 ... ... *** ... ... *** *** *** ... *** *** : *** : *** *** *** ... .000 .000 .000 .000 .000 .005 .051 .279 .663 Standard deviation: = Standard deviation o = /npa n = P = q=