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amm1812
3 years ago
6

The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) (The World Almana

c, 2009): Critical Reading 502 Mathematics 515 Writing 494Assume that the population standard deviation on each part of the test is = 100.a. What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical Reading part of the test (to 4 decimals)?b. What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 515 on the Mathematics part of the test (to 4 decimals)?c. What is the probability a sample of 100 test takers will provide a sample mean test score within 10 of the population mean of 494 on the writing part of the test (to 4 decimals)?
Business
1 answer:
storchak [24]3 years ago
3 0

Answer:

a) P(492

And we can use excel or the normal standard table to find this probability:

P(-0.949 < Z< 0.949)= P(Z

b) P(505

And we can use excel or the normal standard table to find this probability:

P(-0.949 < Z< 1.898)= P(Z

c) P(484

And we can use excel or the normal standard table to find this probability:

P(-1 < Z< 1)= P(Z

Explanation:

Previous concepts

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the scores for critical reading of a population, and for this case we know the distribution for X is given by:

X \sim N(502,100)  

Where \mu=502 and \sigma=100

We select a sample of size n=90, since the distribution for X is normal then the distribution for the sample size is also normal

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}}=\frac{100}{\sqrt{90}}=10.54)

And for this case we want this probability:

P(502-10 < \bar X < 502+10)

And for this case we can use the z score given by:

z= \frac{\bar X -\mu}{\sigma_{\bar x}}

And if we use this formula we got:

P(492

And we can use excel or the normal standard table to find this probability:

P(-0.949 < Z< 0.949)= P(Z

Part b

Let X the random variable that represent the scores for Math of a population, and for this case we know the distribution for X is given by:

X \sim N(515,100)  

Where \mu=515 and \sigma=100

We select a sample of size n=90, since the distribution for X is normal then the distribution for the sample size is also normal

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}}=\frac{100}{\sqrt{90}}=10.54)

And for this case we want this probability:

P(515-10 < \bar X < 515+10)

And for this case we can use the z score given by:

z= \frac{\bar X -\mu}{\sigma_{\bar x}}

And if we use this formula we got:

P(505

And we can use excel or the normal standard table to find this probability:

P(-0.949 < Z< 1.898)= P(Z

Part c

Let X the random variable that represent the scores for Writing of a population, and for this case we know the distribution for X is given by:

X \sim N(494,100)  

Where \mu=494 and \sigma=100

We select a sample of size n=100, since the distribution for X is normal then the distribution for the sample size is also normal

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}}=\frac{100}{\sqrt{100}}=10)

And for this case we want this probability:

P(494-10 < \bar X < 494+10)

And for this case we can use the z score given by:

z= \frac{\bar X -\mu}{\sigma_{\bar x}}

And if we use this formula we got:

P(484

And we can use excel or the normal standard table to find this probability:

P(-1 < Z< 1)= P(Z

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A decrease in consumer spending can be expected to shift the aggregate demand curve ________.
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Answer:

d. downward and cause output to decrease

Explanation:

As we know that

Aggregate demand = Consumption expenditure + government expenditure + net export

Where,

Net export = Export - import

In the case when there is a reduction in the consumer spending so it would be expected that the aggregate demand curve would be shifted to the downward due to which it results in reduction in output

Therefore the option d is correct

6 0
3 years ago
A developer is proposing to build and operate an 8 store strip mall. Each unit would rent for $3,500 per month. It is expected t
lys-0071 [83]

Answer:

<u>Requirement A:</u> CAP Rate is 12.5%

<u>Requirement B:</u> Capitalized Value of the Property is $1,884,960

<u>Requirement C:</u> Loan Amount is $1,413,720

<u>Requirement D:</u> Debt Service Coverage Ratio is 1.85

<u>Requirement E:</u> Loan per unit is $176,715 Per Unit

Explanation:

<u>Requirement A:</u> Find the CAP Rate

The CAP Rate will be calculated using the following formula:

CAP Rate = Annual Net Operating Income (NOI) <u>(Step1)</u> / Property Capitalized Value <u>(Step2)</u>

Here

Operating Income is $235,620 (Step1)

Property Capitalized Value (Step2)

Now, by putting values we have:

CAP Rate = $235,620 / $1,884,960 = 12.5%

<u>Step1:</u> Find Annual Net Operating Income (NOI)

As we know that:

Operating Income = Expected Revenue - Operating Expense

Here

Expected Revenue from 8 Strip Malls = Rent / Month * 12 Months * (1 - Vacancy Ratio) * 8 Strips Malls

= $3,500 * 12 * (1 - 15%) * 8

= $285,600

Operating Expenses = Expected Revenue * 17.5%

= $285,600 * 17.5% = $49,980

Now by putting value in the above Operating Income equation, we have:

Annual Operating Income = $285,600 - $49,980 = $235,620

<u>Step2:</u> Find Property Capitalized Value (It is also <u>Requirement B</u>)

Property Capitalized Value = Annual Operating Income / Minimum Accepted Rate of Return (MARR)

Here

Annual Operating Income is $235,620 from Step1

MARR is 12.5%

By putting values, we have:

Capitalized Value of the Property = $235,620 / 12.5% = $1,884,960

<u></u>

<u>Requirement C. Find Loan Amount</u>

It is given in the question that the Loan Amount is 75% of Property Capitalized Cost. This implies:

Loan Amount = $1,884,960 * 75% = $1,413,720

<u>Requirement D. Debt Service Coverage Ratio</u>

Debt Service Coverage Ratio (DSCR) = Annual Net Operating Income / Total Debt Service for the Year

Here

Annual Net Operating Income is $235,620 from Step1

Total Debt Service for the Year $127,235 (See <u>Step3</u> below)

By putting values, we have:

Debt Service Coverage Ratio = $235,620 / $127,235 = 1.85

<u>Step3: Total Debt Service for the year</u>

Total Debt Service for the year = Loan Amount * Debt Service Rate

Here

Loan Amount is $1,413,720

Debt Service Rate is 9%

By putting values, we have:

Total Debt Service for the year = $1,413,720 * 9% = $127,235

<u>Requirement E. Find Loan Amount</u>

We can find loan per unit by simply dividing the loan amount by number of strip mall. Here total number of strip mall are 8. This implies that:

Loan Per Unit = $1,413,720 / 8 Units = $176,715 Per Unit

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3 years ago
Suppose the economy is at a position below its institutional production possibilities frontier. To improve this situation, Keyne
Cloud [144]

Answer:

Keynesian economists might propose that government <em>reduces </em>taxes, which will cause the aggregate demand curve to shift to the <em>right </em>and Real GDP will <em>increases</em>.

Explanation:

Keynesian economics is demand-sided.

If the economy is producing at full capacity, increased demand will only cause inflation as goods and services cannot be increased although people are willing to pay more (real GDP the same)

However, if the economy is below capacity, the problem is that there is not enough demand to drive production (additional goods and services produced will not be bought). Keynesians would advocate reducing taxes to stimulate demand.

When taxes are reduced, goods become cheaper. People are willing to buy more at similar prices (that producers charge), causing the aggregate demand curve to shift to the <em>right. </em>As economy is below capacity, suppliers are able to responded by supplying more goods and services (supplier curve shift to the right) and Real output (GDP) would increase.

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harkovskaia [24]
I believe the answer is customer satisfaction.
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2 years ago
If the federal government were to run a budget deficit, this would:
Anettt [7]
Answer:
It increases the size of the national debt. <span>When the U.S. </span>federal government runs a budget deficit<span>, it borrows money by selling: Treasury bills, notes, and bonds.</span>

It will help you.
5 0
3 years ago
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