1. Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of each of these variables: Mean SD a) 2X b)4y +2 c) 5x +4y X d) 4x -5y e) X1+ X2 Y a) Find the mean and standard deviation for the random variable 2X. E(2X) 70 25 10 3 SD(2X) (Round to two decimal places as needed.) 2. You draw a card from a deck. If you get a red card, you win nothing. If you get a spade, you win $8. For any club, you get $10plus an extra $20for the ace of clubs. a) Create a probability model for the amount you win at this game. b) Find the expected amount you'll win. c) How much would you be willing to pay to play this game? a) Card red spade ace of clubs any other club Winnings 0 8 30 10 (Type exact answers in simplified form.) 3. An insurance policy costs $130and will pay policyholders $8 000 if they suffer a major injury (resulting in hospitalization) or $3000 if they suffer a minor injury (resulting in lost time from work). The company estimates that 1 in every 2086 policyholders will suffer a major injury and that 1 in 505will suffer a minor injury. a) Create a probability model for the profit on a policy. b) What's the company's expected profit on the policy? c) What's the standard deviation? a) First find the probability and profit for each outcome. x no injury major injury minor injury (Round to six decimal places as needed.) P(event) Profit 4. An employer pays a mean salary for a 5-day workweek of $1200 with a standard deviation of $135. On the weekends, his salary expenses have a mean of $500 with a standard deviation of $61. What is the mean and standard deviation of his total weekly salaries? The mean of his total weekly salaries is $ . (Round to the nearest integer as needed.) 5. Find the standard deviation of the random variable X. x 10 17 2 50 P(X=x x) 0.4 0.2 0.2 0.2 (Round the final answer to the nearest tenth as needed. Round all intermediate values to the nearest thousandth as needed.) 6. In a group of batteries, 6 are dead. You choose 2 batteries at random. a) Create a probability model for the number of good batteries you get. b) What's the expected number of good ones you get? c) What's the standard deviation? a) Create a probability model. Number good 0 P(Number good) ? 1 ? (Round to three decimal places as needed.) 2