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2 years ago

13

James is placing 40.5 inch poster on his 132.75 inch wall. He wants to center the poster horizontally on the wall. How far from

each edge of the wall should be place the poster?

1 answer:

Strike441 [17]2 years ago

7 0

It would be 3.27 inches away from each wall.

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A study was recently conducted at a major university to estimate the difference in the proportion of business school graduates w

sveta [45]

Answer:

$(0.1875-0.274) - 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.1412$

$(0.1875-0.274) + 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.0318$

And the 95% confidence interval would be given (-0.1412;-0.0318).

We are confident at 95% that the difference between the two proportions is between $-0.1412 \leq p_A -p_B \leq -0.0318$

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".

$p_A$ represent the real population proportion for business

$\hat p_A =\frac{75}{400}=0.1875$ represent the estimated proportion for Business

$n_A=400$ is the sample size required for Business

$p_B$ represent the real population proportion for non Business

$\hat p_B =\frac{137}{500}=0.274$ represent the estimated proportion for non Business

$n_B=500$ is the sample size required for non Business

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ 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:

$(0.1875-0.274) - 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.1412$

$(0.1875-0.274) + 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.0318$

And the 95% confidence interval would be given (-0.1412;-0.0318).

We are confident at 95% that the difference between the two proportions is between $-0.1412 \leq p_A -p_B \leq -0.0318$

7 0

1 year ago

A regular pentagon is created using the bases of five congruent isosceles triangles, joined at a common vertex. The total number

Gala2k [10]

It's 54 degrees.

The internet is a wonderful friend. Type in "Pentagon split into triangles" on google images and you will find a diagram that finds it.

4 0

1 year ago

Read 2 more answers

Triangle KLM ~ triangle KQP are similar. Solve for x.

Ymorist [56]

Answer:gui

Step-by-step explanation:

4 0

1 year ago

What is (0.5x + 15) + (8.2x- 16.6)

nadya68 [22]

1.6 I think I’m sorry if it’s incorrect

3 0

1 year ago

Celia bought a bag of 121212 goldfish for \$3$3dollar sign, 3.

muminat

Celia bought a bag of 12 goldfish for $3, Cost of 1 goldfish is $0.25 .

<u>Step-by-step explanation:</u>

The goldfish is a freshwater fish in the family Cyprinidae of order Cypriniformes. It is one of the most commonly kept aquarium fish. A relatively small member of the carp family, the goldfish is native to East Asia.

Here we have , Celia bought a bag of 12 goldfish for $3 . We need to find the cost of 1 goldfish . Let's find out:

Celia have a bag of 12 goldfish which cost her $3 . So , cost of 1 goldfish is equivalent to

⇒ $(1)\frac{12}{3}$

⇒ $(1)\frac{3(4)}{3}$

⇒ $\frac{1}{4}$

⇒ $0.25$

Therefore, Celia bought a bag of 12 goldfish for $3 , Cost of 1 goldfish is $0.25 .

5 0

1 year ago