4. A company is planning to introduce to the market a new brand of soft drink. The
dispensing machine fills the bottles with a volume following normal distribution with mean
µ = 20 ounces and standard deviation σ = .5 ounces.
a. What is the probability that a randomly selected bottle from the production line contains
more than 20.8 ounces of drinks?
b. A state regulation requires that the company labels each bottle showing the volume (in
ounces) of soft drinks in the marketed bottles, and that no more than 2% of the bottles
should contain less than the volume printed on the label. What volume should the company
print on the label in order to comply with the regulation? (Round your answer to 1 decimal
after the decimal point.)
5. The following game is offered in a casino. An employee flips a coin 12 times, but the
player does not see the outcomes of these coin flips. After each flip of the coin the player has
to guess whether the coin turned up head or tail. At the end the player receives k dollars,
where k is the number of correct guesses, except that if she guesses all 12 coin flips correctly,
then she will receive an additional 10,000 dollars (so in that case the total reward will be
10, 000 12 = 10, 012 dollars). Calculate the expected amount of winnings in this game