question 11

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Question 1: Problem 5.99 from your text. Use excel and word to answer this question. Leaking gas tanks. Leakage from underground gasoline tanks at service stations can damage the environment. It is estimated that 25% of these thanks leak. You examine 15 tanks chosen at random. Independently of each other. (a) What is the mean number of leaking tanks in such samples of 15? (b) What is the probability that 10 or more of these 15 tanks leak? (c) Now you do a larger study, examining a random sample of 1000 tanks nationally. What is the probability that at least 275 of these tanks are leaking?

Question 2: Problem 5.109 from your text. Do this problem by hand and scan/take a picture of your work and upload (You may also type your solution up) Testing for HIV. Enzyme immunoassay (EIA) test are used to screen blood specimens for the presence of antibodies to HIV the virus that cause AIDS. Antibodies indicate the presence of the virus. The tests are quite accurate but are not always correct. Here are approximate probabilities of positive and negative EIA outcomes when the blood tested does and does not actually contain antibodies to HIV

Test Results

	Positive	Negative
Antibodies Present	0.9985	0.0015
Antibodies Absent	0.006	0.9994

Suppose that 1% of a large population carries antibodies to HIV in their blood.

(a) Draw a tree diagram for selecting a person from this population (outcomes; EIA positive or negative).

(b) What is the probability that the EIA is positive for a randomly chosen person from this population?

(c) What is the probability that a person has the antibody, given that the EIA test is positive? Comment this exercise illustrates a fact that is important when considering proposals for widespread testing for HIV, illegal drugs, or agents of biological warfare: if the condition being tested is uncommon in the population, many positives will be false positives.

Question 3: Problem 5.110 from the text. Do this problem by hand and scan/take a picture of your work and upload (You may also type your solution up) Testing for HIV continued: the previous exercise gives data on the results of EIA tests for the presence of antibodies to HIV. Repeat part (c ) of that exercise for two different populations.

(a) Blood donors are prescreened for HIV risks factors, so perhaps only 0.1% (0.001) of this population carries HIV antibodies.

(b) Clients of a drug rehab clinic are a high risk group so perhaps 10% of this population carries HIV antibodies.

Question 4: Problem 1.106 from the text. You may just type the answer in a word document or write them down and scan/take a picture of it.

(a) Find the number z such that the proportion of observations that are less than z in a standard normal distribution is 0.8

(b) Find the number z such that the proportion of observations that are less than z in a standard normal distribution are greater than z

Question 5: Problem 1.108 from the text. Do this problem by hand and scan/take a picture of your work and upload (You may also type your solution up) the NCAA considers a student a partial qualifier eligible to practice and receive an athletic scholarship but not to compete if the combined SAT score is a t least 720. Use the information in the previous exercise to find the percent of all SAT scores that are less than 720