Can someone explain to me how to do this and give me the answer?

There are two games involving flipping a coin. In the first game you win a prize if you can throw between 45% and 55% heads. In

Nina [5.8K]

Answer:

d) 300 times for the first game and 30 times for the second

Step-by-step explanation:

We start by noting that the coin is fair and the flip of a coin has a probability of 0.5 of getting heads.

As the coin is flipped more than one time and calculated the proportion, we have to use the <em>sampling distribution of the sampling proportions</em>.

The mean and standard deviation of this sampling distribution is:

$\mu_p=p\\\\ \sigma_p=\sqrt{\dfrac{p(1-p)}{N}}$

We will perform an analyisis for the first game, where we win the game if the proportion is between 45% and 55%.

The probability of getting a proportion within this interval can be calculated as:

$P(0.45$

referring the z values to the z-score of the standard normal distirbution.

We can calculate this values of z as:

$z_H=\dfrac{p_H-\mu_p}{\sigma_p}=\dfrac{(p_H-p)}{\sqrt{\dfrac{p(1-p)}{N}}}=\sqrt{\dfrac{N}{p(1-p)}}*(p_H-p)>0\\\\\\z_L=\dfrac{p_L-\mu_p}{\sigma_p}=\dfrac{p_L-p}{\sqrt{\dfrac{p(1-p)}{N}}}=\sqrt{\dfrac{N}{p(1-p)}}*(p_L-p)$

If we take into account the z values, we notice that the interval increases with the number of trials, and so does the probability of getting a value within this interval.

With this information, our chances of winning increase with the number of trials. We prefer for this game the option of 300 games.

For the second game, we win if we get a proportion over 80%.

The probability of winning is:

$P(p>0.8)=P(z>z^*)$

The z value is calculated as before:

$z^*=\dfrac{p^*-\mu_p}{\sigma_p}=\dfrac{p^*-p}{\sqrt{\dfrac{p(1-p)}{N}}}=\sqrt{\dfrac{N}{p(1-p)}}*(p^*-p)>0$

As (p*-p)=0.8-0.5=0.3>0, the value z* increase with the number of trials (N).

If our chances of winnings depend on P(z>z*), they become lower as z* increases.

Then, we can conclude that our chances of winning decrease with the increase of the number of trials.

We prefer the option of 30 trials for this game.

8 0

2 years ago

What is the value of the discriminant for the quadratic equation -3=-x 2+2x

seraphim [82]

X=3,-1 your answer is right here

3 0

3 years ago

Alana bought 3/8pound of Swiss cheese and 1/4 pounds of American cheese.which pairs of fractions are equivalent to the amounts A

PSYCHO15rus [73]

Is it any fraction? if so 6/16 and 2/8 are equivalent

7 0

3 years ago

Please help !! Which of the following are solutions to the equation below? check all that apply

Gala2k [10]

I thike so i would -4 must help u a lot

7 0

3 years ago

Read 2 more answers

Gus started with a number he multiplied by 8 subtracted 12 divided by 4 and added 7 to get 50 show how to work backward to find

DanielleElmas [232]

Answer:

23

Step-by-step explanation:

This equation can be derived from the question

let a represent the initial number Gus started with

{[(a x 8) - 12] / 4 } + 7 = 50

subtract 7 from both sides of the equation

[(a x 8) - 12] / 4 } = 43

Multiply both sides of the equation by 4

(a x 8) - 12] = 172

Add 12 to both sides

8a =184

Divide both sides by 8

a = 23.

6 0

2 years ago