Download MATH 3070: Worksheet No.10 NAME: 1. A criminologist claims that

MATH 3070: Worksheet No.10
NAME:
1. A criminologist claims that the probability of reform for a first-offender embezzler is 0.9. Suppose
that we define “reform” as meaning the person commits no criminal offenses within a five-year
period. Three paroled embezzlers were randomly selected from the prison records, and their
behavioral histories were examined for the five-year period following prison release.
(a) Is it a binomial experiment? If so, identify the probability p of each trial, and the number n
of trials in the experiment.
(b) Find the frequency function, and construct the graph of probability distribution.
(c) If the criminologist's claim is correct, what is the probability that all three were reformed?
At least two?
2. A drug company has 50 potential new prescription drugs under clinical test. 30% of all drugs that
reach this stage are eventually licensed for sale.
(a) Is it a binomial experiment? If so, identify the probability p of each trial, and the number n
of trials in the experiment.
(b) Identify the normal distribution which approximates the binomial distribution.
(c) What is the probability that less than 9 of the 50 drugs are eventually licensed?
(d) What is the probability that at least 22 are eventually licensed?
3. A survey of 100 tractor-trailer units passing through a weighing station confirmed that 38 had a
potentially serious braking system problem.
(a) Identify the “success” of each trial, and the number n of trials in the experiment.
(b) Estimate the success probability p, and construct a 95% confidence interval.
(c) The researcher wants to investigate that more than 1 in 3 tractor-trailer units has an
imminently hazardous mechanical condition related to the breaking system. State the null
hypothesis and the alternative hypothesis.
(d) Present your findings.
4. Researchers obtained a sample of 20 crayfish from a lake to estimate the proportion of crayfish that
exhibit more than five (ppb) units of mercury. Of those sampled, 11 exceeded five units.
(a) Identify the “success” of each trial, and the number n of trials in the experiment.
(b) Estimate the success probability p, and construct a 95% confidence interval.
(c) Does the data indicate that more than a half of crayfish are seriously contaminated with
mercury? State the null hypothesis and the alternative hypothesis.
(d) Present your findings.
5. A survey from random samples of 200 Republicans and 200 Democrats showed that 109
Republicans and 86 Democrats were in favor of tax incentives.
(a) Is the proportion of Republicans in favor of tax incentives is greater than the proportion of
Democrats? Construct he null hypothesis and the alternative hypothesis.
(b) Give the significance level for your test, and state your conclusion.