On Valentine's Day the Quiet Nook restaurant offers a Lucky Lovers Special that could save couples money on their romantic dinners. When the waiter brings the check he also brings a scratch-off ticket that the couple scrapes to reveal a hidden number; call this number X. The value of the number X is the dollar amount that will be subtracted from their dinner bill. The possible values of the scratch-off number X are shown in the table below. The table also shows the probability distribution of the values of X. Dlscount ValueX 0 9 19 25 29 Probability 0.25 0.30 0.25 0.10 0.10 i Question 1. Find the expected value of the discount X. H\" Question 2. Find the standard deviation of the discount X.(Use 2 decimal places.) H\" For the past several weeks the restaurant has also been distributing coupons worth $5 off any dinner for two. The coupon can be used in addition to the discount X from the scratch-off ticket. If every couple dining there on Valentine's Day also brings a $5 coupon, what are the expected value and standard deviation of the total discount the couples receive? Question 3. Expected value of total discount. U\" Question 4. Standard deviation of total discount U\" When two couples dine together on a single check, the restaurant doubles the scratch-off discount X; so the discount values are 2X, that is, twice the amounts shown in the above table. (the $5 discount coupon cannot be used). Question 5. What is the expected value of the discount for 2 couples? U\" Question 6. What is the standard deviation of the discount for 2 couples? H\