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Korolek [52]
3 years ago
6

According to a recent​ survey, the population distribution of number of years of education for​ self-employed individuals in a c

ertain region has a mean of 15.1 and a standard deviation of 4.8.
a. Identify the random variable X whose distribution is described here.
b. Find the mean and the standard deviation of the sampling distribution of x overbar for a random sample of size 36. Interpret them.
c. Repeat​ (b) for nequals144. Describe the effect of increasing n.
Mathematics
1 answer:
adell [148]3 years ago
6 0

Answer:

a)  X that is a distribution of number of years of education for​ self-employed individuals.

b) Mean = 15.1, Standard Deviation = 0.8

c) Mean = 15.1, Standard Deviation = 0.4

Step-by-step explanation:

We are given the following in the question:

The population distribution of number of years of education for​ self-employed individuals in a certain region has a mean of 15.1 and a standard deviation of 4.8

a) The random variable is X that is a distribution of number of years of education for​ self-employed individuals.

b) According to central limit theorem, as the sample size increases the distribution of means approaches a normal distribution.

Thus, \bar{x} has a normal distribution with

\text{Mean} = 15.1\\\text{Srtandard Deviation} = \displaystyle\frac{\sigma}{\sqrt{36}} = \frac{4.8}{\sqrt{36}} = 0.8

c) n = 144

\bar{x} has a normal distribution with

\text{Mean} = 15.1\\\text{Srtandard Deviation} = \displaystyle\frac{\sigma}{\sqrt{n}} = \frac{4.8}{\sqrt{144}} = 0.4

By increasing n, the standard deviation for distribution of mean reduced  by one half. Therefore, we see that quadrupling the sample size will reduce the standard deviation by one half.

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Step-by-step explanation:

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2 years ago
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4.
Juli2301 [7.4K]
<h3>Answer:  6 ounces</h3>

========================================================

Work Shown:

(6 servings)/(4 oz of sauce) = (8 servings)/(x oz of sauce)

6/4 = 8/x

6*x = 4*8

6x = 32

x = 32/6

x = 5.333 approximately

x = 6 we round up despite 5.333 being closer to 5, than it is to 6.

If we went with 5 ounces, then we wouldn't clear the hurdle needed to serve 8 people.

The section below goes over why this is the case in more detail.

---------

6 servings : 4 ounces

6/4 servings : 4/4 ounces

1.5 servings : 1 ounce

So one ounce of sauce gets us 1.5 servings.

If we multiply both sides by 5, then,

1.5 servings : 1 ounce

5*1.5 servings : 5*1 ounce

7.5 servings : 5 ounces

This shows that 5 ounces of sauce will only produce 7.5 servings, which comes up short compared to 8 servings.

If we multiplied both sides by 6, then

1.5 servings : 1 ounce

6*1.5 servings : 6*1 ounce

9 servings : 6 ounces

This shows that 6 ounces of sauce yields 9 servings. We've gone overboard, but it's better to do that than come up short.

3 0
3 years ago
Is this answer right?
Dmitrij [34]

Answer:

  Blank 1: 64° (or 32°, depending on what the label applies to)

  Blank 2: 42

Step-by-step explanation:

It is a common mistake to believe you have solved the problem when you have found the value of the variable(s) in the problem. You have correctly found the values of n (42) and m (9). However, that is not what the problem is asking for.

We cannot tell if the value (1/2n+11)° is referring to angle DAB, or to angle CAB. In any event, (1/2n+11)° = (1/2×42 +11)° = 32°.

If that is angle CAB, then angle DAB is twice that value, 64°.

If that is angle DAB, then angle DAB is 32°.

__

The side length CD is the same as any other side length in a rhombus, so ...

  CD = 4m+6 = 4×9 +6

  CD = 42 . . . . units

3 0
3 years ago
The logo for Chris's Calculator Company is 3 semicircles. The logo will be placed on the company building and will be 4 feet tal
Keith_Richards [23]

Answer:

The area of the logo is 18.84\ ft^{2}

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The area of a semicircle is equal to

A=\frac{1}{2}\pi r^{2}

so

The area of the logo is equal to multiply by 3 the area of one semicircle

A=\frac{3}{2}\pi r^{2}

we have

r=4/2=2\ ft -----> the radius is half the diameter

substitute

A=\frac{3}{2}(3.14)(2)^{2}=18.84\ ft^{2}

8 0
3 years ago
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