Suppose a miniature golf player sinks a hole-in-one about 12% of the time on any given hole and is going to play 8 games at 18 h
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Answer:
(A) The minimum sample size required achieve the margin of error of 0.04 is 601.
(B) The minimum sample size required achieve a margin of error of 0.02 is 2401.
Step-by-step explanation:
Let us assume that the percentage of support for the candidate, among voters in her district, is 50%.
(A)
The margin of error, <em>MOE</em> = 0.04.
The formula for margin of error is:
The critical value of <em>z</em> for 95% confidence interval is:
Compute the minimum sample size required as follows:
Thus, the minimum sample size required achieve the margin of error of 0.04 is 601.
(B)
The margin of error, <em>MOE</em> = 0.02.
The formula for margin of error is:
The critical value of <em>z</em> for 95% confidence interval is:
Compute the minimum sample size required as follows:
Thus, the minimum sample size required achieve a margin of error of 0.02 is 2401.
Answer:
Step-by-step explanation:
We will use the right Riemann sum. We can break this integral in two parts.
We take the interval and we divide it n times:
The area of the i-th rectangle in the right Riemann sum is:
For the first part of our integral we have:
For the second part we have:
We can now put it all together:
![\sum_{i=1}^{i=n} [(\Delta x)^4 i^3-6(\Delta x)^2i]\\\sum_{i=1}^{i=n}[ (\frac{3}{n})^4 i^3-6(\frac{3}{n})^2i]\\ \sum_{i=1}^{i=n}(\frac{3}{n})^2i[(\frac{3}{n})^2 i^2-6]](https://tex.z-dn.net/?f=%5Csum_%7Bi%3D1%7D%5E%7Bi%3Dn%7D%20%5B%28%5CDelta%20x%29%5E4%20i%5E3-6%28%5CDelta%20x%29%5E2i%5D%5C%5C%5Csum_%7Bi%3D1%7D%5E%7Bi%3Dn%7D%5B%20%28%5Cfrac%7B3%7D%7Bn%7D%29%5E4%20i%5E3-6%28%5Cfrac%7B3%7D%7Bn%7D%29%5E2i%5D%5C%5C%0A%5Csum_%7Bi%3D1%7D%5E%7Bi%3Dn%7D%28%5Cfrac%7B3%7D%7Bn%7D%29%5E2i%5B%28%5Cfrac%7B3%7D%7Bn%7D%29%5E2%20i%5E2-6%5D)
We can also write n-th partial sum:
We take the interval and we divide it n times:
The area of the i-th rectangle in the right Riemann sum is:
For the first part of our integral we have:
For the second part we have:
We can now put it all together:
We can also write n-th partial sum: