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Solnce55 [7]
3 years ago
8

The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the e

ighth grade level. In an earlier study, the population proportion was estimated to be 0.21. How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 85% confidence level with an error of at most 0.03
Mathematics
1 answer:
irakobra [83]3 years ago
6 0

Answer:

We need a sample size of at least 383.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

85% confidence level

So \alpha = 0.15, z is the value of Z that has a pvalue of 1 - \frac{0.15}{2} = 0.925, so Z = 1.44.

How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 85% confidence level with an error of at most 0.03

We need a sample size of at least n.

n is found with M = 0.03, \pi = 0.21

Then

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.03 = 1.44\sqrt{\frac{0.21*0.79}{n}}

0.03\sqrt{n} = 1.44\sqrt{0.21*0.79}

\sqrt{n} = \frac{1.44\sqrt{0.21*0.79}}{0.03}

(\sqrt{n})^{2} = (\frac{1.44\sqrt{0.21*0.79}}{0.03})^{2}

n = 382.23

Rounding up

We need a sample size of at least 383.

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3.75 or 15/4

Step-by-step explanation:

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3 years ago
My area is 93 x 81. what is the square footage
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What you do is you do 93 x 81.

                             93
                          x 81
                      ------------
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That's the square footage. Hope it helps!
5 0
3 years ago
A geometric sequence has a first term of 3 and a fourth term of 81÷8.<br><br> Find the eighth term
tatuchka [14]

Answer:

6561 / 128

Step-by-step explanation:

The nth term of a geometric sequence is:

a = a₁ (r)ⁿ⁻¹

The first term is 3, and the fourth term is 81/8.

81/8 = 3 (r)⁴⁻¹

27/8 = r³

r = 3/2

The eighth term is therefore:

a = 3 (3/2)⁸⁻¹

a = 6561 / 128

5 0
3 years ago
FIND BD !!!!!!!!!!!!!!!!!!!!
Viktor [21]

BD = 2x-4

But it's also BE - CE + CD

BE is 3x-1

CE is 2x-3

CD is 2

so

BD = 3x-1 -(2x-3) +2

simplified

BD = 1x +4

since BD = BD (obviously), we can also say that the righthand sides of the two equation must be equal

2x -4 = 1x +4

let's solve for x and that put it into either of the 2 equations.

2x -4 = 1x +4

subtract 1x on both sides

x -4 = 4

add 4 on both sides

x = 8

substitute x for its value in 2x -4 = 1x +4

(this way we double check BD in two expressions at once. the equation should come out true, meaning same value for BD in each expression. both sides should be equal).

2*8 -4 = 1*8 +4

12 = 12

seems true

BD is safely 12

4 0
3 years ago
What is the solution set to the following system x+y=5
Agata [3.3K]
<h3>Answer:</h3>

D (0, 5), (5, 0)

<h3>Step-by-step explanation:</h3>

Anything with -5 and 0 will not satisfy x+y=5. This eliminates the first three choices.

___

It is easiest to check the offered answers. You can also solve this graphically, or by solving the simultaneous equations.

You can, for example, square the first equation and subtract the second:

... (x+y)² -(x²+y²) = 5² -25

... 2xy = 0

This will be true for x=0 or for y=0, so (0, 5) and (5, 0) are solutions to the pair of equations.

3 0
3 years ago
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