LAMC Math 137 Test 3 Module 5 Yun 11/14/2014

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1 LAMC Math 137 Test 3 Module 5 Yun 11/14/2014 Last name First name You may use a calculator but not a cellphone, tablet or an ipod. Please clearly mark your choices on multiple choice questions and box your answers on free response questions. 20 pts. 1. For many years the only way to test if a person had tuberculosis (TB) required a laboratory procedure that could take up to several weeks to produce a definite result. There are now DNAbased tests to detect TB that can be done in a couple of hours. We have the following data on a DNA test for TB If a person does not have TB then the DNA test always is negative. If a person does have TB, then the DNA test will be positive 94% of the time. Assume that we will use the test in Africa where the rate of incidence of TB is 650 per 100,000. (a) What is the value of Q? (b) What is the value of P? (c) Find the probability that a person does not have TB? (d) Find the probability that a person that receives a negative test result actually does have TB, that is, find the P(TB given a negative test). 0 out of 99,350 = 0 27 out of 99,577 = / = / 650 =

2 21 pts. 2. A local Honda dealership collects data on customers. Here is data from 311 customers who purchased a Honda Civic. (a) The number of females in the sample who purchased a Honda Civic is (b) The total number of people in the sample who purchased a standard-engine Honda Civic is (c) The number of males in the sample who purchased a hybrid Honda Civic is (d) What percentage of the people purchased a standard-engine Honda Civic? 77 out of 194, about 40% 111 out of 311, about 36% 34 out of 117, about 29% 200 out of 311, about 64% (e) Which of the following probability statements is found with the computation 117 / 194? P(male and standard engine) P(female male) P(standard engine male) P(male standard engine) (f) What does the data suggest about the relationship between gender and engine type? Women are less likely to purchase a Honda Civic with a standard engine than men. Women and men are equally likely to purchase a Honda Civic with a standard engine. Women are more likely to purchase a Honda Civic with a standard engine than men. Men are more likely to purchase a Honda Civic with a standard engine than men. 2

3 20 pts. 3. Here are the results of a survey that students conducted at a mall. The students conducted this survey as part of a statistics project to determine if younger adults are more likely to have tattoos (a) We randomly select a person who responded to this survey. Which calculation gives the probability that the person has at least one tattoo? 765 out of out of out of out of 505 (b) If we randomly select a person in the sample who is 18 to 29 years old, what is the probability that this person has a tattoo? (c) If we randomly select a person in the sample, what is the probability that this person is 18 to 29 years old and has a tattoo? (d) Which proportions are most useful in analyzing the relationship between age and tattoos? 170 / 490 and 60 / / 490 and 445 / / 230 and 320 / / 230 and 60 / 230 (e) If we randomly select a person in the sample, what is the probability that this person is 18 to 29 years old or has no tattoo?

4 24 pts. 4. The following table summarizes the full-time enrollment at a community college located in a West Coast city. There are a total of 12,000 full-time students enrolled at the college. The two categorical variables here are gender and program. The programs include academic and vocational programs at the college. Assume that a student can enroll in only one program. (a) What proportion of the total number of students are male students? (b) What proportion of the total number of students are Bus-Econ students? (c) If a male student is selected at random, what is the probability that he is in the Health Sciences program? (d) If a student is selected at random, what is the probability that the student is female and in the Bus- Econ program? (e) Suppose a student in the InfoTech program is selected at random. What is the probability that the student is female? (f) Find P(Info Tech I male) 4

5 15 pts. 5. The table below is based on a 1988 study of accident records conducted by the Florida State Department of Highway Safety. (a) (b) Based on this data, the risk of a fatal accident is very small whether you are wearing a seat belt or not. Do you think this statement is valid or invalid? Explain your reason. (c) The risk of a fatal accident for those wearing seat belts and those not wearing seat belts are given below: P(fatality I seat belt) = and P(fatality I no seat belt) = Use the formulato caluculate the percentchage. 5