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It is known that the population variance equals 484. With a .95 probability, the sample size that needs to be taken if the desir

Ksju [112]

Answer:

We need a sample size of at least 75.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.025 = 0.975$ , so $z = 1.96$

Now, we find the margin of error M as such

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

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

The standard deviation is the square root of the variance. So:

$\sigma = \sqrt{484} = 22$

With a .95 probability, the sample size that needs to be taken if the desired margin of error is 5 or less is

We need a sample size of at least n, in which n is found when M = 5. So

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

$5 = 1.96*\frac{22}{\sqrt{n}}$

$5\sqrt{n} = 43.12$

$\sqrt{n} = \frac{43.12}{5}$

$\sqrt{n} = 8.624$

$(\sqrt{n})^{2} = (8.624)^{2}$

$n = 74.4$

We need a sample size of at least 75.

6 0

4 years ago

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How many 1 fourths are in 3 fourths?

Mama L [17]

Answer:

12

Step-by-step explanation:

This question means 3/(1/4). The rule for division of fractions is invert the denominator and multiply. 3/(1/4) = 3 * 4 = 12. Another way to think of it is to imagine you have 3 pies each divided into quarters.

7 0

3 years ago

For which value of theta is sine theta = negative 1?

Ivan

Answer:

1) 270 degrees

2) pi/4 rad

Step-by-step explanation:

1.) For which value of theta is sine theta = negative 1?

Given

sintheta = -1

theta = arcsin(-1)

theta = -90degrees

Since sin is negative in the third and 4th quadrant

In the third quadrant, theta = 180 + 90 = 270degrees

In the fourth quadrant, theta = 360 - 90 = 270 degrees

Hence the required value of theta is 270degrees

2) Given the radius of the circle to be 1, the y axis value will also be 1 units

Opposite = 1

adjacent = 1

hyp = √1²+1²

hyp = √2

sin theta = opp/hyp

sin theta = 1/√2

theta = arccsin(1/√2)

theta = 45 degrees

Express in radians

45 degrees = pi/4 radians

Hence the required angle in the first quadrant is pi/4 rad

4 0

3 years ago

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A psychologist collects data on the time, w, in minutes, people walk each day and their scores, t ,on a stress test. The scores

faust18 [17]

Answer: D: The model predicts that a person who does not walk each day will score about 48.1 on the test.

Step-by-step explanation:

Given: A psychologist collects data on the time, w, in minutes, people walk each day and their scores, t ,on a stress test.

She finds that there is a negative linear association between w and t that is best modeled by the equation $t=-2.5w+48.1$ .

When we put w=0 minutes, t=48.1

It implies that if any patient doesn't walk will score 48.1.

Hence, the model predicts that a person who does not walk each day will score about 48.1 on the test.

8 0

3 years ago

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Help extra points really important to me

Naily [24]

Answer:

a.7(6xy-2z)

=7*6xy-7*2z

=42xy-14z

b.5(2w+3)-6(w+2)

=5*2w+5*3-6*w-6*2

=10w+15-6w-12

=4w+3

c.2f(2f+g-3)

=2f*2f+2f*g-2f*3

=4f^2+2fg-6f

Step-by-step explanation:

7 0

3 years ago

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Look at photo asap please