Is (1, 2) solution for this system of inequalities ?

A random sample of 1000 people was taken. Four hundred fifty of the people in the sample favored Candidate A. The 95% confidence

KatRina [158]

Answer:

The 95% confidence interval would be given (0.419;0.481).

Step-by-step explanation:

Data given and notation

n=1000 represent the random sample taken

X=450 represent the people in the sample favored Candidate A

$\hat p=\frac{450}{1000}=0.45$ estimated proportion of people in the sample favored Candidate A

$\alpha=0.05$ represent the significance level

Confidence =0.95 or 95%

p= population proportion of people in the sample favored Candidate A

Solution to the problem

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.5=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.45 - 1.96 \sqrt{\frac{0.45(1-0.45)}{1000}}=0.419$

$0.45 + 1.96 \sqrt{\frac{0.45(1-0.45)}{1000}}=0.481$

And the 95% confidence interval would be given (0.419;0.481).

We are confident (95%) that about 41.9% to 48.1% of the people are favored Candidate A.

3 0

3 years ago

When the health department tested private wells in a county for two impurities commonly found in drinking water, it found that 1

aleksley [76]

Answer:

P(Y= 0) = 0.1

P(Y= 0) = 0.7

P(Y= 0) = 0.2

Step-by-step explanation:

Let Y be number of impurities that can be found in the well,

Let A denote the event that impurity A is randomly found in the well

Here Y can have three values i.e 0 , 1 and 2

✓It will take take the value of 0 when there is no impurity found in the well

✓It will take the value of 1 when when exactly one impurity vis found in the well

✓It will take the value of 2 when when both impurities vis found in the well

CHECK THE ATTACHMENT FOR DETAILED EXPLATION

6 0

3 years ago

What is the missing base 256 = ^4

Inessa05 [86]

So the problem is $256=x^4$ and you need to find x.

You can find x by taking fourth root of 256. The easiest way is to use your calculator. On my scientific calculator, it is 2nd then the button ^ that is $\sqrt[x]{}$
You get the answer of 4.

3 0

4 years ago

A rectangular prism had a volume of 540 cubic centimeters. the height of this prism was changed from 10 centimeters to 5 centime

levacccp [35]

The volume of the new rectangular prism would be 270 cubic centimeters. The reason for this is that when only one dimension is changed, the overall volume is only changed by that same relationship. Because only the height was cut in half, this would be only one of the dimensions.

3 0

4 years ago

Three numbers are in the ratio of 2:3:4 and their LCM are 240. Their HCF is?<br>

Dmitrij [34]

Answer:

20.

Step-by-step explanation:

Assign variables. The numbers acan be 2x, 3x and 4x. Then, LCM of 2x, 3x and 4x is 12x

12x = 240

(240/12) = x = 20

The HCF of 2x, 3x, and 4x is 20. (Because x is the highest common factor.)

7 0

3 years ago