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Mama L [17]
2 years ago
5

The SAT is the most widely used test in the undergraduaté admissions process, Scores on the math portion of the SAT are believed

to
be normally distributed and range from 200 to 800. A researcher from the admissions department at the University of New Hampshire
is interested in estimating the mean math SAT scores of the incoming class with 95% confidence. How large a sample should she take
to ensure that the margin of error is below 20?
(You may find it useful to reference the z table. Round intermediate calculations to at
least 4 decimal places and "2" value to 3 decimal places. Round up your final answer to the nearest whole number.)
Mathematics
1 answer:
Anvisha [2.4K]2 years ago
6 0

Using the z-distribution, it is found that she should take a sample of 97 scores to ensure that the margin of error is below 20.

<h3>What is a z-distribution confidence interval?</h3>

The confidence interval is:

\overline{x} \pm z\frac{\sigma}{\sqrt{n}}

In which:

  • \overline{x} is the sample mean.
  • z is the critical value.
  • n is the sample size.
  • \sigma is the standard deviation for the population.

The margin of error is given by:

M = z\frac{\sigma}{\sqrt{n}}

Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800, hence by the Empirical Rule the standard deviation is given by:

6\sigma = 800 - 200

\sigma = 100

In this problem, we have a 95% confidence level, hence\alpha = 0.95, z is the value of Z that has a p-value of \frac{1+0.95}{2} = 0.975, so the critical value is z = 1.96.

To ensure a margin of error of 20, we solve for n when M = 20, hence:

M = z\frac{\sigma}{\sqrt{n}}

20 = 1.96\frac{100}{\sqrt{n}}

20\sqrt{n} = 1.96 \times 100

\sqrt{n} = 1.96 \times 5

(\sqrt{n})^2 = (1.96 \times 5)^2

n = 96.04.

Rounding up, she should take a sample of 97 scores to ensure that the margin of error is below 20.

More can be learned about the z-distribution at brainly.com/question/25890103

#SPJ1

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omeli [17]

Answer:

  • x = - 6

Step-by-step explanation:

A hole is an input value that makes both numerator and denominator equal to zero.

<u>Let's factorize the numerator and denominator:</u>

  • 3x² - 108 = 3(x² - 36) = 3(x + 6)(x - 6)
  • x² + 2x - 24 = x² + 6x - 4x - 24 = x(x + 6) - 4(x + 6) = (x - 4)(x + 6)

<u>We have same factor of x + 6:</u>

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  • x = - 6 is a hole
8 0
2 years ago
Simplify the expression
Molodets [167]

Answer:

8x^8/3 y^4 - The first option

Step-by-step explanation:

The first thing we need to do is the exponent outside the bracket and leave the 8 till last, because exponents always come before multiplying coefficients. When an term with an exponent is multiplied by another exponent outside a bracket, the exponents of both terms are multiplied by the exponent outside the bracket.

This means that the expression is now:

8(x^2*4/3 y^3*4/3)

First we can so the x term. The x term already has an exponent of 2, so the 2 is multiplied by the 4/3 exponent outside the bracket. 2*4/3 = 8/3, so the x term is now: x^8/3

The same happens to the y term: 3*4/3 simplifies to 4, so the y term is now y^4.

So now our expression is:

8(x^8/3 y^4)

Now the 8 outside the bracket simply multiplies on to the whole term so we finish with:

8x^8/3 y^4 - The first option.

Hope this helped!

7 0
3 years ago
What two numbers multiply to get -36 and add to get 5
attashe74 [19]
-4 x 9= -36 and the when you add 5 to -36 you get -31. Hope this helps
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Step-by-step explanation:

5/10+2/10

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