MATH 131 Mini-Test II Due: noon Monday, June 12, 2017 Dr. Molitierno Name: Directions: Please SHOW YOUR WORK. Not showing work seriously jeopardizes your chance of getting credit for your answer. 1. (18pts) Data on the 5000 largest mutual funds shows which funds provided a high 5-year return and a high 10-year return. Of the 5000 mutual funds surveyed, 4000 funds had a high 5-year return, 1800 had a high 10-year return, and 1200 had both a high 5-year return and a high 10-year return. (a) What is the probability of a mutual fund having a high 5-year return or a high 10-year return? (b) Given that a mutual fund had a high 5-year return, what is the probability of a mutual fund having a high 10-year return? (c) Are a mutual fund having a high 5-year return and a mutual fund having a high 10-year return dependent or independent events? EXPLAIN. 2 2. (20pts) We roll two dice, one right after the other. Each die has five sides. The first die we roll has sides numbered 1, 2, 3, 3, 4. The second die we roll has sides numbered 1, 2, 4, 5, 7. We are interested in the total of the dice. Below is a chart that gives the total of the two dice rolled. Observe there are 25 possible outcomes: second roll f irst roll 1 2 3 3 4 1 2 3 4 4 5 2 3 4 5 5 6 4 5 6 7 7 8 5 7 6 8 7 9 8 10 8 10 9 11 (a) What is the probability that we roll a total less than or equal to 8? (b) What is the probability that we roll a total greater than or equal to 6? (c) What is the probability that we roll a total greater than or equal to 6 given that our first roll is a 3? (d) Are the events \"rolling a total greater than or equal to 6\" and \"the first roll is a 3\" dependent or independent events? EXPLAIN. 3 3. (20pts) A sample of 600 respondents was selected to determine if geography has an effect on political affiliation (either Republican or Democrat). Of the 350 midwesterners who took this survey, 280 said they are Republican. Of the 250 people who live on a coast who took this survey, 110 said they are Democrat. (a) Fill in the following contingency table: Political Party Republican Democrat Total Midwestern Coastal Total (b) What is the probability that a person is a Republican? (c) Given that a person is a midwesterner, what is the probability that he/she is a Republican? (d) Are living in the midwest and being a Republican independent events? EXPLAIN. 4 4. (42pts) The average age for a person getting married is 32 years. Assume the ages for getting married have a normal distribution with a standard deviation of 4 years. (a) What is the probability that a person gets married when he/she is 27 years of age or younger? (b) What is the probability that a person gets married when he/she is 34 years of age or older? (c) What is the probability that a person gets married between 29 and 33 years of age? 5 (d) Before what age do 58% of people get married? (e) After what age do 72% of people get married? (f) Between what two ages symmetrically distributed about the mean do 83% of people get married