1. Recognizing Mutually Exclusive Events In Exercises 1-6, decide if the events are mutually exclusive. Write M (upper case) for mutually exclusive and N(upper case) for non-mutually exclusive. 1. Event A: Randomly select a female public school teacher. Event B: Randomly select a public school teacher who is 25 years old. 2. Event A: Randomly select a member of the U.S. Congress. Event B: Randomly select a male U.S. Senator. 3. Event A: Randomly select a student with a birthday in April. Event B: Randomly select a student with a birthday in May. 4. Event A: Randomly select a person between 18 and 24 years old. Event B: Randomly select a person who drives a convertible. 5. Event A: Selecting a week in which overtime wages were paid Event B: Selecting a week in which temporary help wages were paid. 6. Event A: Selecting a week in which overtime wages were paid. Event B: Selecting a week in which no wages were paid. 2. You select a family with three children. Let M represents a male child and F a female child. Round all answers to 4 decimal places. a) The sample space for this experiment has outcomes? b) Let B = The Number of Boys. Complete the probability distribution for B. B=b P(B = b) Use your probability distribution to answer the following questions. A family is selected at random, find the probability that they have: c) Two boys d) at least one male child. e) either one male or three males f) No girls. 3. The number of crimes reported (in millions) and the number of arrests reported (in millions) by the U.S. Department of Justice for 14 years (Adapted from the National Crime Victimization Survey and Uniform Crime Reports) Enter Y for yes and N for no a) Is a strong positive correlation between crimes, x, and arrests, y? b) Can the regression equation be considered to be very useful for making predictions? 4. The number of crimes reported (in millions) and the number of arrests reported (in millions) by the U.S. Department of Justice for 14 years (Adapted from the National Crime Victimization Survey and Uniform Crime Reports) a) Find the regression equation that models the number of crimes as a function of the number of arrests is y = ___ x + ____ b) The correlation coefficient is R2 = c) The linear correlation coefficient is R = d) SST = e) SSR = f) SSE = ROUND ALL ANSWERS TO 4 DECIMAL PLACES X.XXXX