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1 year ago

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The coordinate plane shows the floor plan for a swimming pool. What is the area of the pool’s border? A. 50 square meters B. 65

square meters C. 80 square meters D. 100 square meters E. 125 square meters Reset Next

1 answer:

podryga [215]1 year ago

7 0

Answer: Choice B

Step-by-step explanation:

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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 recent survey of 8,000 high school students found that the mean price of a prom dress was $195.00 with a standard deviation of

KiRa [710]

To calculate the z-statistic, we must first calculate the standard error.

Standard error is standard deviation divided by the square root of the population. In this case, it is equal to 2.68.

The z-score is defined the distance from the sample to the population mean in units of standard error.

z = (195 – 208)/2.68 = -4.86

5 0

1 year ago

A truck delivers 478 dozen eggs to stores in one day. Write an expression that finds the number of eggs the truck delivers in on

7nadin3 [17]

478*12= answer which the answer is: 5736

4 0

2 years ago

Read 2 more answers

Abel is making brownies for a bake sale. The recipe shows the amount of each ingredient needed to make 9 brownies. Complete each

mixas84 [53]

Answer:

In order to make 45 brownies, Abel needs 25 cups of flour, 20 cups of sugar, 10 cups of cocoa powder and 5 eggs.

Step-by-step explanation:

As the recipe is missing in this question, the recipe is found online which given following information

Abel needs 5 cups of flour to make brownies.
If Abel uses 4 cups of sugar.
he will need to use 2 cups of cocoa powder.
The recipe will make brownies if Abel uses only 1 egg.

Abel has to make 45 brownies for the sale, this is also missing in this question, however is given in the reference question linked here.

This recipe is to make 9 brownies. Now for 45 brownies the multiplier is found as 45/9=5. So by multiplying quantity of all the ingredients by 5, Abel will be able to make 45 brownies.

Now in order to make 45 brownies

Abel needs 5*5 =25 cups of flour to make brownies.
If Abel uses 5*4=20 cups of sugar.
he will need to use 5*2=10 cups of cocoa powder.
The recipe will make brownies if Abel uses only 5*1=5 egg.

So in order to make 45 brownies, Abel needs 25 cups of flour, 20 cups of sugar, 10 cups of cocoa powder and 5 eggs.

5 0

2 years ago

The following data represent the length of life in

Natali [406]

Answer:

(a) For the stem-and-leaf plot, we need to organise all data in columns, one column is the stem and a second column is the leaf, but in this case, stems are going to be the digits to the left of the decimal point, and leafs are the digits to the right of the decimal point:

<u>Stem</u> <u> Leaf </u>

0 2 2 2 3 3 4 5 7

1 0 2 3 5 5 8

2 0 3 5

3 0 3

4 0 5 7

5 0 5 6 9

6 0 0 0 5

(b) Relative frequency distribution.

Remember that, a relative frequency is calculated dividing the absolute frequency by the total data, in this case, we approximated to the hundredth.

Length of life Absolute Frequency Relative Frequency % Relative Freq.

0.2 3 0.1 10

0.3 2 0.07 7

0.4 1 0.03 3

0.5 1 0.03 3

0.7 1 0.03 3

1.0 1 0.03 3

1.2 1 0.03 3

1.3 1 0.03 3

1.5 2 0.07 7

1.8 1 0.03 3

2.0 1 0.03 3

2.3 1 0.03 3

2.5 1 0.03 3

3.0 1 0.03 3

3.3 1 0.03 3

4.0 1 0.03 3

4.5 1 0.03 3

4.7 1 0.03 3

5.0 1 0.03 3

5.5 1 0.03 3

5.6 1 0.03 3

5.9 1 0.03 3

6.0 3 0.10 10

6.5 1 0.03 3

Total 30

(c)

To calculate the sample mean we need to sum all number, which results: 83.9. Then, we divide this result to the total 30, which result: 2.80.

The sample range is the difference between the highest and the lowest value: 6.5 - 0.2 = 6.3.

The sample standard deviation is calculated trough the following process:

Step 1: Subtract the mean from each number.

Step 2: Square each result.

Step 3: Add the squared deviations.

Step 4: Divide the sum by one less the total.

Step 5: Take the square root, and there you have it.

Doing this steps, the result is 2.22.

This last process is attached:

4 0

1 year ago