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Aliun [14]
3 years ago
14

A roulette wheel has the numbers 1 through 36, 0, and 00. A bet on four numbers pays 8 to 1 (that is, if you bet $1 and one of t

he four numbers you bet comes up, you get back your $1 plus another $8). How much do you expect to win with a $1 bet on four numbers? HINT [See Example 4.] (Round your answer to the nearest cent.)
Mathematics
1 answer:
Natasha_Volkova [10]3 years ago
4 0

Answer:

Lose $0.05

Step-by-step explanation:

There are 38 possible spots on the roulette wheel (numbers 1 to 36, 0 and 00).

If the player can choose four numbers on single $1 bet, his chances of winning (W) and losing (L) are as follows:

P(W) = \frac{4}{38} \\P(L) = 1-P(W) = 1-\frac{4}{38} \\P(L) = \frac{34}{38}

The expected value of the bet is given by the probability of winning multiplied by the payout ($8), minus the probability of losing multiplied by the bet cost ($1)

EV=\frac{4}{38}*\$8 -\frac{34}{38}*\$1\\EV= -\$0.05

On each bet, the player is expected to lose 5 cents ($0.05).

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Answer:

9

Step-by-step explanation:

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Heights of men have a bell-shaped distribution, with a mean of 176 cm and a standard deviation of 7 cm. Using the Empirical Rule
Vaselesa [24]

Answer:

a) 68% of the men fall between 169 cm and 183 cm of height.

b) 95% of the men will fall between 162 cm and 190 cm.

c) It is unusual for a man to be more than 197 cm tall.

Step-by-step explanation:

The 68-95-99.5 empirical rule can be used to solve this problem.

This values correspond to the percentage of data that falls within in a band around the mean with two, four and six standard deviations of width.

<em>a) What is the approximate percentage of men between 169 and 183 cm? </em>

To calculate this in an empirical way, we compare the values of this interval with the mean and the standard deviation and can be seen that this interval is one-standard deviation around the mean:

\mu-\sigma=176-7=169\\\mu+\sigma=176+7=183

Empirically, for bell-shaped distributions and approximately normal, it can be said that 68% of the men fall between 169 cm and 183 cm of height.

<em>b) Between which 2 heights would 95% of men fall?</em>

This corresponds to ±2 standard deviations off the mean.

\mu-2\sigma=176-2*7=162\\\\\mu+2\sigma=176+2*7=190

95% of the men will fall between 162 cm and 190 cm.

<em>c) Is it unusual for a man to be more than 197 cm tall?</em>

The number of standard deviations of distance from the mean is

n=(197-176)/7=3

The percentage that lies outside 3 sigmas is 0.5%, so only 0.25% is expected to be 197 cm.

It can be said that is unusual for a man to be more than 197 cm tall.

3 0
3 years ago
Ryker is given the graph of the function y= 1/2x^2 - 4 . He wants to find the zeros of the function but is unable to read them e
REY [17]
y = \frac{1}{2x^{2} - 4}
0 = \frac{1}{2x^{2} - 4}
0(2x^{2} - 4) = (2x - 4)(\frac{1}{2x^{2} - 4})
0(2x^{2}) - 0(4) = 1
0 - 0 = 1
0\neq1
8 0
3 years ago
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