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
Gennadij [26K]
3 years ago
5

Suppose an article reported that 14% of unmarried couples in the United States are mixed racially or ethnically. Consider the po

pulation consisting of all unmarried couples in the United States. (a) A random sample of n = 100 couples will be selected from this population and p, the proportion of couples that are mixed racially or ethnically, will be computed. What are the mean and standard deviation of the sampling distribution of p? (Round your answer for μp to two decimal places and your answer for σp to four decimal places.)
Mathematics
1 answer:
Anvisha [2.4K]3 years ago
8 0

Answer: \mu_{\hat{p}}=0.14 and \sigma_{\hat{p}}=0.0347

Step-by-step explanation:

In sampling distribution of \hat{p}.

The mean and standard deviation of the sampling distribution of p is given by :-

\mu_{\hat{p}}=p

\sigma_{\hat{p}}=\sqrt{\dfrac{p(1-p)}{n}}  , where p= population proportion and n= sample size.

Let p be the population proportion of unmarried couples in the United States are mixed racially or ethnically.

As per given , we have

n = 100

p= 14% =0.14

Then, the mean and standard deviation of the sampling distribution of p will be :

\mu_{\hat{p}}=0.14

\sigma_{\hat{p}}=\sqrt{\dfrac{0.14(1-0.14)}{100}}

\sigma_{\hat{p}}=\sqrt{\dfrac{0.14(0.86)}{100}}

\sigma_{\hat{p}}=\sqrt{\dfrac{0.1204}{100}}

\sigma_{\hat{p}}=\sqrt{0.001204}

\sigma_{\hat{p}}=0.0346987031458\approx0.0347

Hence, the required answer : \mu_{\hat{p}}=0.14 and \sigma_{\hat{p}}=0.0347

You might be interested in
PLEASE HELP ASAP PLZ
adoni [48]

Answer:

dont listen to person above me . it's a scam

5 0
3 years ago
Staci is attending a music festival. The ticket to the festival costs $87.96 . Staci plans to purchase $30.00 t-shirts from the
mafiozo [28]

Step one: 200-87.96=112.04

Step two: 112.04÷30≈3.7

Step three: 3.7↔3

Answer: Staci can buy 3 shirts

5 0
3 years ago
Of the total population of American households, including older Americans and perhaps some not so old, 17.3% receive retirement
Alex Ar [27]

Answer:

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

Step-by-step explanation:

We use the binomial aproxiation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be solved using 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.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

p = 0.173, n = 120. So

\mu = E(X) = np = 120*0.173 = 20.76

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{120*0.173*0.827} = 4.14

In a random sample of 120 households, what is the probability that more than 20 households but fewer than 35 households receive a retirement income?

We are working with discrete values, so this is the pvalue of Z when X = 35-1 = 34 subtracted by the pvalue of Z when X = 20 + 1 = 21.

X = 34

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

Z = \frac{34 - 20.76}{4.14}

Z = 3.2

Z = 3.2 has a pvalue of 0.9993

X = 21

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

Z = \frac{21 - 20.76}{4.14}

Z = 0.06

Z = 0.06 has a pvalue of 0.5239

0.9993 - 0.5239 = 0.4754

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

6 0
3 years ago
Day Drive 270 miles and 6 hours how many miles do you drive in 13 hours ​
NikAS [45]

Answer:

The answer is

<h2>585 miles</h2>

Step-by-step explanation:

In order to solve this question we use ratio and proportion

From the question

Day Drive 270 miles in 6 hours

So in order to find the distance drove in 13 hours, we compare the distance drove in 6 hours to the distance drove in 13 hours and solve

That's

if in 6 hours Day drove 270 miles

Then in 13 hours the person will drive

\frac{13  \times 270}{6}  =  \frac{3510}{6}

We have the final answer as

<h3>585 miles</h3>

Hope this helps you

7 0
3 years ago
What is the solution for a + 5 and two-thirds = 9
erastova [34]

Answer:

8.5

Step-by-step explanation:

Do you mean "(a+5)2/3

(a + 5) 2/3 = 9

a + 5 = 13.5

a=8.5

3 0
3 years ago
Other questions:
  • 72 feet is equal to how many yards?
    5·1 answer
  • Write the quadratic equation in standard form.
    8·2 answers
  • What is the area of the parallelogram?
    7·2 answers
  • A rectangular prism has sides that are in the ratio of 3:5:9. If the volume of the prism is 8640 cm3, then the surface area of t
    8·1 answer
  • Is it true that 5 2/3 -3 3/4 equals 1+2/3+3/4?
    14·1 answer
  • Which ordered pairs are solutions to the inequality y−4x≤−6y−4x≤−6 ? select each correct answer. (3, 5)(3, 5) (−2, −14)(−2, −14)
    5·1 answer
  • Alex is thinking of a number.
    5·1 answer
  • A magician will perform her magic tricks as long as there are more than 15 people in the audience a. P &gt; 15 b. P&lt; 15 c. P
    13·1 answer
  • Can you please elaborate on this question? I'm unable to visualize what has been told.
    7·1 answer
  • 2. (01.01 LC)
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!