Have you ever tried to get out of jury duty? About 25% of those called will find an excuse (work, poor health, travel out of town, etc.) to avoid jury duty†. If 15 people are called for jury duty, find the following. a) What is the probability that all 15 will be available to serve on the jury? (Round your answer to three decimal places.)(b) What is the probability that 9 or more will not be available to serve on the jury? (Round your answer to three decimal places.)(c) Find the expected number of those available to serve on the jury. What is the standard deviation? (Round your answers to two decimal places.)μ =σ =(d) How many people n must the jury commissioner contact to be 95.9% sure of finding at least 12 people who are available to serve? (Enter your answer as a whole number.)

Step-by-step explanation:

a) About 25% of those called will find an excuse (work, poor health, travel out of town, etc. to avoid jury duty. So, the probability that a jury will be available to serve is ; P = 1 - q = 1 - 0.25 = 0.75

Given n = 15 and  p = 0.75

P(X = 15) = Binompdf(15, 0.75, 15) = 0.013

b) Event "9 or more will not be available to serve on the jury" is equivalent to "6 or less will be available to serve".

P(X ≤ 6) = Binompdf(15, 0.75, 6) = 0.004

c) The expected number and the standard deviation of those available to serve on the jury are: μ = np = 15(0.75) = 11.25

σ = √np(1 - p) = √15(0.75)(1 - 0.75) = 1.68

d) Use function:

P(X ≥ 12) = 1 - P(X ≤ 11) = 1 - Binompdf(n, 0.75, 11)

By using above function, the probabilities of P(X ≥ 12) at different sample size are shown below:

nP(X ≥ 12)

120.032

130.127

140.281

150.461

160.630

170.765

180.861

190.923

200.959

210.979

Therefore, The jury commissioner must contact at least 20 people to be 95.9% sure of finding at least 12 people who are available to serve.

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step-by-step explanation: