statistics/probability
posted by carmen, please help!! on .
A game consists of tossing two coins, first a dime and then a nickel. For each coin which comes up a head you win the value of the coin. For each coin which comes up a tail you get nothing.
{HH,HT,TH,TT}  each outcome with probability .25  winnings are 15,10,5,0
a) Find the mean or expected winnings
b) Find the standard deviation of your winnings.
c) If you had to pay a dime to play the game, what would be the mean of your winnings?
d) If you had to pay a dime to play the game, what would be the standard deviation of your winnings?

Expected winning can be found by summing over all possible outcomes the product of winning and the respective probability.
For outcome HH:
winning=0.25
probability = 0.25
prodcut = 0.25*0.25=0.0625
Repeat for the 3 other outcomes, and add the 4 products together to get the expected winning. 
The breaking strength (in pounds) of a certain new synthetic is normally distributed, with a mean of 170 and a variance of 4. The material is considered defective if the breaking strength is less than 166 pounds. What is the probability that a single, randomly selected piece of material will be defective?