1. (a) Make a histogram showing the probabilities of

r= 0, 1, 2, 3,,

8and9defective syringes in a random sample ofninesyringes.Recall that the binomial distribution with parametersn,p, andrgives the probability distribution of the number ofrsuccesses in a sequence ofntrials, each of which yields success with probabilityp. Here we can let "success" be defined as "finding a defective syringe." The batch contains1%defective syringes, so there is a1%chance that any given syringe will be found to be defective. Therefore,p= . A random sample ofninesyringes are checked for quality, son= .

2. USA Todayreports that about 25% of all prison parolees become repeat offenders. Alice is a social worker whose job is to counsel people on parole. Let us say success means a person does not become a repeat offender. Alice has been given a group of four parolees.(a) Find the probabilityP(r) ofrsuccesses ranging from 0 to 4. (Round your answers to three decimal places.)

P(0) =

P(1) =

P(2) =

P(3) =

P(4) =

(b) Make a histogram for the probability distribution of part (a).

(c) What is the expected number of parolees in Alice's group who will not be repeat offenders? parolees What is the standard deviation? (Round your answer to two decimal places.) parolees (d) What is the smallest group Alice can counsel to be at least 98% sure that three or more parolees will not become repeat offenders? parolees

3. 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) If12people are called for jury duty, what is the probability that all12will be available to serve on the jury? (Round your answer to three decimal places.) (b) If12people are called for jury duty, what is the probability that6or more willnotbe 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 standard deviation to two decimal places.)

= people

= people

(d) What is the smallest number of peoplenthat the jury commissioner contact to be at least 95.9% sure of finding at least 12 people who are available to serve? (Enter your answer as a whole number.) people