If you laid one of each size bolt 3/8, 1/2, 5/8, 7/8 and 1 1/4 end to end how long would the row of bolts be

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

Solve i=Prt for t, if i=105,p=700,and r=0.05

Katen [24]

3675. You multiply 105 700, then you multiply the answer by 0.05.

5 0

3 years ago

Read 2 more answers

Which shows the correct substitution of the values ab and c from the equation 0 = - 3x ^ 2 - 2x + 6 into the quadrati formula?

scZoUnD [109]

The answer would look something like this:

$\frac{2+-\sqrt{2^{2}-4(-3)(6) }}{2(-3)}$

There could also have a simplified version.

I hope this helps.

7 0

3 years ago

A pre-image and its image under a translation have the same orientation?

Black_prince [1.1K]

Answer:

In a translation, ALL of the points move the same distance in the same direction. A translation is called a rigid transformation or isometry because the image is the same size and shape as the pre-image.

Step-by-step explanation:

In addition, the corresponding segment sides of the pre-image and image are parallel.

8 0

2 years ago

Translate the sentence into an inequality. Twice the difference of a number and 7 is at most −20 . Use the variable y for the un

3241004551 [841]

If the number is y then the inequality is
twice the difference of y and 7=2(y-7)
at most- 20=less than or equal to
2(y-7)≤-20

5 0

3 years ago