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3 years ago

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Imagine performing a coin-flip experiment in which the coin is "loaded" in such a way that the probability of landing heads is t

wice greater than tails. after tossing the coin 10 times, what is the probability of observing a heads only on the 2nd and 8th toss?

1 answer:

myrzilka [38]3 years ago

8 0

IM SORRY I CANT HELP YOU ONE THIS ONE SORRY I HOPE THIS HELPS :)

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You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard devia

Arturiano [62]

Answer:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (3)

$n=(\frac{2.58(54.5)}{5})^2 =790.846 \approx 791$

So the answer for this case would be n=791 rounded up to the nearest integer

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that $z_{\alpha/2}=2.58$

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (2)

And on this case we have that ME =+5 and we are interested in order to find the value of n, if we solve n from equation (2) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (3)

$n=(\frac{2.58(54.5)}{5})^2 =790.846 \approx 791$

So the answer for this case would be n=791 rounded up to the nearest integer

4 0

3 years ago

Use the arc length formula to find the length of the curve y = 4x − 5, −1 ≤ x ≤ 2. check your answer by noting that the curve is

professor190 [17]

Ok, here we go. Pay attention. The formula for the arc length is $AL= \int\limits^b_a { \sqrt{1+( \frac{dy}{dx})^2 } } \, dx$ . That means that to use that formula we have to find the derivative of the function and square it. Our function is y = 4x-5, so y'=4. Our formula now, filled in accordingly, is $AL= \int\limits^2_1 { \sqrt{1+4^2} } \, dx$ (that 1 is supposed to be negative; not sure if it is til I post the final answer). After the simplification we have the integral from -1 to 2 of $\sqrt{17}$ . Integrating that we have $AL= \sqrt{17}x$ from -1 to 2. $2 \sqrt{17}-(-1 \sqrt{17} )$ gives us $3 \sqrt{17}$ . Now we need to do the distance formula with this. But we need 2 coordinates for that. Our bounds are x=-1 and x=2. We will fill those x values in to the function and solve for y. When x = -1, y=4(-1)-5 and y = -9. So the point is (-1, -9). Doing the same with x = 2, y=4(2)-5 and y = 3. So the point is (2, 3). Use those in the distance formula accordingly: $d= \sqrt{(2-(-1))^2+(3-(-9))^2}$ which simplifies to $d= \sqrt{9+144}= \sqrt{153}$ . The square root of 153 can be simplified into the square root of 9*17. Pulling out the perfect square of 9 as a 3 leaves us with $3 \sqrt{17}$ . And there you go!

5 0

2 years ago

4) What is the present value of $4000 received at the

Bingel [31]

Answer:

$11040

Step-by-step explanation:

first of all the question says that $4000 were earned in a year and asks for what the new vale would be after the next 3 years with a discount rate of 8%.

If 1 year=$4000,then 3 years=$12000

100%-8%=92% (this happens because there is still a remaining amount that still has a cost to it),so 12000*92%=$11040

8 0

3 years ago

Read 2 more answers

What is the value of the 10th term in this arithmetic sequence? <br><br>2,5,8,11,...

yKpoI14uk [10]

It looks to be 29, if the rule is to add 3z

8 0

3 years ago

What is the solution to the equation below?<br><br><br><br> 0.5n = 6

Tcecarenko [31]

It's 12 because if you divide 6 by 0.5 you should get 12, so basically use the opposite operation.

Hope that helps!

3 0

3 years ago