Question

1.Joe is playing a game of chance at the hibiscus festival, costing $1 for each game. In the game two fair dice are rolled and the sum of the numbers that turned up is found. If the sum is seven, then Joe wins $5. Otherwise loses his money. Joe play the game 15 times. Find his expected profit or lose?

2. The basketball player has a 75% chance of a successful shot. The shots are assumed to be independent of each other. Find the probability that 3 out of the next 4 shots are successful?

3.

1. The weight of potatoes produced by one particular farm are found to be approximately normally distributed, with the mean weight of 147 g and a standard deviation of 23g.
2. i. What proportion of the potatoes produced by this farm will weigh less than 160 g?
   ii. Of all the potatoes produced on the farm, 5% are considered too light. What is the maximum weight that will be considered too light?
3. The amounts of electricity bills for all households in a city have a skewed probability distribution with mean of $140 and a standard deviation of $30. Find the probability that the mean amount of electric bills for a random sample of 75 households selected from the city will be within $6 of the population mean

Answer 1

(1)

S = {(1, 1), (1, 2), (1, 3) ... (6, 4), (6, 5), (6, 6)} and n(S) = 36

A = Sum is 7 = {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)} and n(A) = 6

P(Win) = n(A)/n(S) = 6/36 = 1/6 = 0.1667

P(Lose) = 1 - 0.1667 = 0.8333

Profit (x)	P(x)
$4	0.1667
$-1	0.8333

Expected profit per game = $4 * 0.1667 + $-1 * 0.8333 = $-0.1667

In 15 games, Joe is expected to lose 15 * $0.1667 = $2.50

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