Question

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.†

(a) If 12 people are called for jury duty, what is the probability that all 12 will be available to serve on the jury? (Round your answer to three decimal places.)

(b) If 12 people are called for jury duty, what is the probability that 6 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.)

? =

o =

(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.)

Answer 1

The number of people available to serve follows binomial distribution with

a)Here the probability .

b) 6 or more will not be available to serve for duty is

The R command for the above probability is

> 1-pbinom(5,12,0.25)

[1] 0.05440223
>

c) The expecetd number of those available to serve on the jury is

Standard deviation is

.

d)We need .

Consider the following R commands.

> 1-pbinom(12,75,0.25)
[1] 0.9569257

> 1-pbinom(12,76,0.25)
[1] 0.9621631

Clearly .