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NikAS [45]
3 years ago
11

16)

Mathematics
1 answer:
HACTEHA [7]3 years ago
3 0
Is the x in between the 5 and 6 supposed to be a multiplication symbol?<span />
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Your friend Alex is planning a fundraising game night to raise money for a local children's hospital. She invites a few of your
katrin [286]

Step-by-step explanation:

(a) You win $5 if you roll a six, $1 if you roll an odd number, and $0 if you roll a 2 or a 4, and you pay $1.50 for every roll.  The expected value is the sum of each outcome multiplied by its probability.

E = (5.00)(1/6) + (1.00)(3/6) + (0)(2/6) + (-1.50)(1)

E = -0.167

You are expected to lose on average about $0.17 per roll, which means Alex has the advantage.

(b) The probability of rolling a 2 or 4 on a fair die is 2/6 or 1/3.  The probability of this happening five times is:

P = (1/3)⁵

P = 1/243

P ≈ 0.41%

There is approximately a 0.4% probability that a fair die will roll a 2 or 4 five times.

(c) The confidence interval for a proportion is:

CI = p ± ME

ME = CV × SE

The margin of error is the critical value times the standard error.

The critical value for 95% confidence is z = 1.960.

The standard error for a proportion is:

SE = √(pq/n)

Given p = 1/6, q = 5/6, and n = 100:

SE = √((1/6) (5/6) / 100)

SE = 0.037

So the confidence interval is:

CI = 1/6 ± (1.960) (0.037)

CI = 0.167 ± 0.073

0.094 < p < 0.240

Since the observed proportion of 0.08 is outside of this interval, we can conclude with 95% confidence that the die is not fair.

(d) Under the current game rules and die probabilities, the expected value is:

E = (5.00)(0.08) + (1.00)(0.33) + (0)(0.59) + (-1.50)(1)

E = -0.77

To make the game fairer, but to still give Alex the advantage so she can make money for her fundraiser, we need to change the rules of the game so that the expected value is less negative.

One simple way to do this is to pay players $2.00 if they roll a 2.

Now the expected value is:

E = (5.00)(0.08) + (1.00)(0.33) + (2.00)(0.29) + (0)(0.30) + (-1.50)(1)

E = -0.19

Now instead of expecting to lose on average $0.77 per roll, players can expect to lose on average $0.19 per roll.  This means they have a better chance of winning money, but Alex still has the advantage.

8 0
3 years ago
Which one is right can y help me
Vlad [161]

Answer:

What are you trying to find out? Like what do you mean by which one is right?

Step-by-step explanation:

7 0
2 years ago
How are the key features of a quadratic graph seen
Tpy6a [65]
Ye ye cuz fat is fat it mix and make ye ye and fat and I use fat to cook my dog but sometimes I air fry hey you reading stop being stressed abt homework and go air fry ur dog U won’t regret it
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3 years ago
Which expression is equivalent to (3x² + 4x - 7)(x - 2)? (Apex)
katovenus [111]

Answer:

A i think

Step-by-step explanation:

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A 747 airplane is 762 inches tall how tall is it in feet
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Divide by 12 BC it really be like that sometimes
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