Question

1. Have you ever tried to get out of jury duty? About 25% of those called will have an excuse to avoid jury duty. If 12 people are called for jury duty:
   1. What is the probability that all 12 will be available to serve on the jury?
   2. What is the probability that 6 or more will not be available to serve on the jury?

Find the expected number (average number) of those available to serve on the jury? What is the standard deviation

Answer 1

Let & demotes the number people who will have seuse to avoid jury duty. The sample size = 12 The prob. that will not be available to serve on the darling en p = 0.25 .: X~ Bimomial (m-12, p =0-28) Pm f 2 x is P(x = x) = ne pronon- n ato = 0.25 0.750 x0,1,,...,12 a) Probability that all 12 will be available to serve on the jwey - Prob. that no people will be available to serve on the jury, is P(x=0) = 12exo 25x0.75 00317 b) The prob. that 6 och more will not be available to serve on the jury is P/X2, 6) - 1-P(x=0) - P(x-1)-P(x - 2) - P(x-2) - P(x-4) - P(x =5) =1120 25 x 0.75² - 2x 0.25% 0.25" - 12 x 0.25 +0.750 - 2x0.25 .79 0.25 x 0.75

- 1 0 25 X 675 sit = 1- O'0347 5 012673 -0.2323~0.1787 -0:1936-01032 = 10:13381 The expected number to serve on the jury - 12x (10:25) = 19 ) of ei those available m (1-P) Standard deviation oa m (1-1) = 1 12x075*0.25 12xo 75x0.25