Statistics Assignment page 1 of 1 Computing Means and Variances 1. You're taking a multiple-choice exam and you don't know the answers to two of the questions. Each question has four choices, so the probability of getting a question right by guessing Is .25. Draw a tree diagram showing the probabilities of getting none, one, or both questlons right by guessing. (3 points) 2. Using the tree diagram you just constructed, make a table showing the probability distribution of getting zero, one, or both questions right by guessing. (3 points) 3. Find the expected value of the number of questions you'd get right by guessing. What are the variance and standard deviation? (3 points) 4. Let's say that for one of the two questions you can narrow the answer choices down to three. Now your chance of getting that question right by guessing is g. What is the new expected value for the number of questions you'd get right by guessing? What are the new variance and standard deviation of this random variable? Drawing another tree diagram and making another probability distribution table may help you answer this question. (3 points) 5. You have a continuous random variable X, for which the mean ,u equals 2.71. You apply the transformation X"I = 5 -- 3x to the values of the random variable. What is the mean of the transformed variable? (3 points) 6. The variance for the same random variable from question 5 is 1.22. After applying the transformation from question 5, what is the new variance? What is the standard deviation of the transformed random variable? (3 pomts) 7. Your friend has two jobs. She works a different number of hours each week, so her paycheck for each job Is different from week to week. Her average weekly paycheck is $110 for job one and $75 for job two. What is her average weekly income if these are her only jobs? (3.5 points) 8. Your friend's parents each have a job. Her mother's average weekly salary is $740 with a standard deviation of $43. Her father's average weekly salary is $535, with a standard deviation of $25. Find the average weekly salary of her parents combined, and the standard deviation of their combined salaries. You can assume that the amount of money her mother makes has no effect on her father's salary, and vice versa. (3.5 points)