Explain whether the differences between what occurred and what you
might expect by chance is statistically significant, implications?
1. 500 tosses of a coin you see 30 tails
2. 85% free throw shooter(basketball)makes 24 of 30 freethrows
3. It rains in Phoenix for 5 days in a row in August
4. Someone gives you 10 to 1 odds that you cannot roll a double number
with the roll of a pair of dice. You win $10 if you succeed and you
lose $1 if you fail. What is the expected value of the game for you?
Should you expect to win or lose the first game? What can be expected
if you play 100 times?
5. Lottery, Assume the jackpot has a value of $30 million, you spend
$365 per year, tickets are $1, with odds at 1 in 80,000,000 for top
prize, $100,000 1 in 1,900,000, $5,000 1 in 365,000, $100 1 in 8,800
$7 1 in 207, $4 1 in 200, $3 1 in 75. What is the expected value of
the winnings for a sinlge lottery ticket if you spend $365 per year?
How much can you expect to win or lose?
6. Mean Household Size, It's estimated that 57% of Americans live in
households with 1 or 2 people, 32% live in households with 3 or 4
people and 11% live in households with 5 or more. Explain how you will
find the expected number of people in an american household. How is
this related to the mean household size?
7. Roulette, House edge. The probability of winning when you bet on a
single number in roulette is 1 in 38 A $1 bet yields a net gain of $35
if it wins.
a. suppose that you bet $1 on the single number 23. What is your
probability of winning? What is the expected value of this bet to you?
b. You bet $1 on numbers 8,13 & 23. What is your probability of
winning? what is the expected value of this bet to you?
c. Compare the results of parts a & b. Does the expected value change
with the number of numbers on which you bet? |
