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.

Discount Value X 1 10 19 25 29 Probability .25 .30 .25 .10 .10

Question 2. Find the standard deviation of the discount X.(Use 2 decimal places.)

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 4. Standard deviation of total discount

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 6. What is the standard deviation of the discount for 2 couples?