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1 month ago

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According to a "how to stop bullying" Web site, 15% of students report experiencing bullying one to three times within the most

recent month. Let's assume the standard deviation is 4.5% of students. Joseph collects data from 186 students at a medium-sized school in Iowa and finds that only 11% reported this rate of bullying. What is his 95% confidence interval?

1 answer:

PIT_PIT [12.4K]1 month ago

4 0

Answer:

His 95% confidence interval spans (0.065, 0.155).

Step-by-step explanation:

In a sample comprising n individuals surveyed with a success probability of $\pi$ , and a confidence level of $1-\alpha$ , the following confidence interval of proportions is established.

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

In which

z represents the z-score associated with a p-value of $1 - \frac{\alpha}{2}$ .

For this scenario, we have:

$n = 186, \pi = 0.11$

At a 95% confidence level

Thus $\alpha = 0.05$ , z is the specific Z-value that holds a p-value of $1 - \frac{0.05}{2} = 0.975$ , consequently $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.11 - 1.96\sqrt{\frac{0.11*0.89}{186}} = 0.065$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.11 + 1.96\sqrt{\frac{0.11*0.89}{186}} = 0.155$

His 95% confidence interval is (0.065, 0.155).

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If mJI = (3x+2)°, mHLK = (15x-36)°, and m∠HML = (8x-1)°, find mHLK

lawyer [12517]

Response:

The measure of mHLK is "(204)°".

Step-by-step breakdown:

Given values include:

mJI = (3x+2)°

mHLK = (15x-36)°

and,

m∠HML = (8x-1)°

then,

What is mHLK?

Now,

Utilizing the chord-chord angle formula, we find

$mHMK=\frac{1}{2}(mJL+mHLK)$

Inserting the known values into the equation gives us

⇒ $(8x-1)=\frac{1}{2}(15x-36+3x+2)$

By carrying out cross-multiplication, we arrive at

⇒ $2(8x-1)=18x-34$

⇒ $16x-2=18x-34$

By subtracting "18x" from both sides, we obtain

⇒ $16x-2-18x=18x-34-18x$

⇒ $-2x-2=-34$

Upon adding "2" to both sides, we end up with

⇒ $-2x=-34+2$

⇒ $-2x=-32$

⇒ $x=\frac{32}{2}$

⇒ $x=16$

By substituting the value of "x" into mHLK = (15x-36)°, we calculate

⇒ (15x-36)° = (15×16-36)°

⇒ = (240-36)°

⇒ = (204)°

Thus, mHLK = (204)°

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First note the ratio is
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Answer:

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Step-by-step explanation:

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substitute values into the equation and resolve for the radius r

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