1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Dafna11 [192]
3 years ago
15

Juries should have the same racial distribution as the surrounding communities. According to the U.S. Census Bureau, 18% of resi

dents in Minneapolis, Minnesota, are African Americans. Suppose a local court will randomly sample 100 state residents and will then observe the proportion in the sample who are African American. How likely is the resulting sample proportion to be between 0.066 and 0.294 (i.e., 6.6% to 29.4% African American)
Mathematics
1 answer:
Ymorist [56]3 years ago
3 0

Answer:

0.997 = 99.7% probability that the resulting sample proportion to be between 0.066 and 0.294

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

18% of residents in Minneapolis, Minnesota, are African Americans. Suppose a local court will randomly sample 100 state residents and will then observe the proportion in the sample who are African American.

This means that p = 0.18, n = 100

So, by the Central Limit Theorem:

\mu = 0.18, s = \sqrt{\frac{0.18*0.82}{100}} = 0.0384

How likely is the resulting sample proportion to be between 0.066 and 0.294?

This is the pvalue of Z when X = 0.294 subtracted by the pvalue of Z when X = 0.066. So

X = 0.294

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{0.294 - 0.18}{0.0384}

Z = 2.97

Z = 2.97 has a pvalue of 0.9985

X = 0.066

Z = \frac{X - \mu}{s}

Z = \frac{0.066 - 0.18}{0.0384}

Z = -2.97

Z = -2.97 has a pvalue of 0.0015

0.9985 - 0.0015 = 0.997

0.997 = 99.7% probability that the resulting sample proportion to be between 0.066 and 0.294

You might be interested in
Atherine has $54. She plans to spend more than $20 of the money for a painting canvas. The rest will go toward paints. Each tube
horsena [70]

I think that she could buy 3 tubes of paint because that's $25.50 and that gives you 28.50 for the canvas.

4 0
3 years ago
Drag the correct steps into order to solve the equation -7x + 14 = 56 for x.
Lina20 [59]

Answer:

-7x + 14 = 56

Subtract 14 both sides

-7x + 14 - 14 = 56 - 14

-7x = 42

Divide both sides by -7

(-7x)/(-7) = 42/(-7)

x = -6

3 0
3 years ago
Read 2 more answers
2.5 divided by 0.5 what would that be
Alex17521 [72]

Answer:

1.25

Step-by-step explanation:

1/2 of 2.5 is 1.25

Think of it as the following

250 divided by 2 is 125 because 125+125=250

4 0
2 years ago
Read 2 more answers
345 degrees to a radion​
miv72 [106K]

We convert degrees to radian by multiplying by  (

\frac{\pi}{180})

=  (345)  ×  (  \frac{\pi π}{180} )

=  (\frac{345}{180})  ×  (π)

=  1.9166π

=  1.9166  ×  3.14

=  6.018 rad

≈  6.02 rad

4 0
3 years ago
What is the result of adding these two equations?
timofeeve [1]

Answer:

the result of adding these two equations is

3x = 14

Step-by-step explanation:

We are given two equations

5x − y  = 6          eq. 1

−2x + y = 8        eq. 2

Add the like terms together

5x - 2x = 3x

− y + y = 0

6 + 8 = 14

So the result of adding these equations is

3x + 0 = 14

3x = 14

Bonus:

The value of x is

3x = 14

x = 14/3

6 0
3 years ago
Other questions:
  • I need help I need help I need help
    8·2 answers
  • Sophia is 8 years older than Lila. Twenty years ago Sophia was three times as old as Lila. How old is each now?
    10·2 answers
  • <img src="https://tex.z-dn.net/?f=80%20-%202w%20%5Cgeqslant%2050" id="TexFormula1" title="80 - 2w \geqslant 50" alt="80 - 2w \ge
    8·1 answer
  • Type the correct answer in the box. Spell all words correctly.
    5·1 answer
  • What is (5.2 × 10^2) × (1.2 × 10^4)?    A. 6.4 × 10^8   B. 6.24 × 10^8   C. 6.4 × 10^6   D. 6.24 × 10^6
    10·2 answers
  • A dog and a cat are 200 meters apart when they see each other. The dog can run at a speed of 30 m/sec, while the cat can run at
    10·2 answers
  • Write the function tan(<img src="https://tex.z-dn.net/?f=%5Cfrac%7B3%5Cpi%20%7D%7B4%7D%20-x" id="TexFormula1" title="\frac{3\pi
    5·1 answer
  • Help me with this equation please
    8·1 answer
  • if two parents have 6 children what is the probability that they will have exactly 5 daughters and one son? (assume that boys an
    15·1 answer
  • How many three-digit even numbers are possible if the leftmost digit cannot be zero?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!