Answer:
80 telephones should be sampled
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.
![\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=%5Cpi%20%5Cpm%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
In which
z is the z-score that has a p-value of
.
The margin of error is of:
![M = z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
89% confidence level
So
, z is the value of Z that has a p-value of
, so
.
How many telephones should be sampled and checked in order to estimate the proportion defective to within 9 percentage points with 89% confidence?
n telephones should be sampled, an n is found when M = 0.09. We have no estimate for the proportion, thus we use ![\pi = 0.5](https://tex.z-dn.net/?f=%5Cpi%20%3D%200.5)
![M = z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
![0.09 = 1.6\sqrt{\frac{0.5*0.5}{n}}](https://tex.z-dn.net/?f=0.09%20%3D%201.6%5Csqrt%7B%5Cfrac%7B0.5%2A0.5%7D%7Bn%7D%7D)
![0.09\sqrt{n} = 1.6*0.5](https://tex.z-dn.net/?f=0.09%5Csqrt%7Bn%7D%20%3D%201.6%2A0.5)
![\sqrt{n} = \frac{1.6*0.5}{0.09}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%20%5Cfrac%7B1.6%2A0.5%7D%7B0.09%7D)
![(\sqrt{n})^2 = (\frac{1.6*0.5}{0.09})^2](https://tex.z-dn.net/?f=%28%5Csqrt%7Bn%7D%29%5E2%20%3D%20%28%5Cfrac%7B1.6%2A0.5%7D%7B0.09%7D%29%5E2)
![n = 79.01](https://tex.z-dn.net/?f=n%20%3D%2079.01)
Rounding up(as 79 gives a margin of error slightly above the desired value).
80 telephones should be sampled
Answer:
14 apples, 10 bananas
Step-by-step explanation:
.07 * 12 = .84 (12 apples at 7 pence/per = 84 pence)
5 - .84 = 4.16 (4.16 pound remaining)
4.16/.4 = 10.4 (you can buy 10 bananas with 4.16 pounds, with .16 pence remaining)
.16 / .7 = 2.3 (you can buy two more apples with 16 pence)
Hope this helps.
Answer:
A. 37.5% less than B
Step-by-step explanation:
We can write an equation to model this:
B being 60% more than A means that:
B=0.6A+1A
B=1.6A
Let's isolate A.
A=B/1.6
Multiply the top and bottom by 10 to get whole numbers
A=10B/16
Simplify
A=5B/8
5/8 = 62.5%
A=0.625B
Therefore, A is 62.5% of B
This means that A is 37.5% less than B.
Answer:
68.
Step-by-step explanation:
The common difference d = -19 - (-22) = 3
So the 31st term =
a31 = -22 + (31-1)3
= -22 + 90
= 90 - 22
= 68.