The sample​ mean, x ​, is a statistic.
True or False

Answer:

a) By the Central Limit Theorem, it has an approximately normal shape, with mean(center) 0.9 and standard deviation(spread) 0.035.

b) Average numbers of children between 0.83 and 0.97 are reasonably likely in the sample.

c) 0.0021 = 0.21% probability that the average number of children per family in the sample will be 0.8 or less

d) 0.9958 = 99.58% probability that the average number of children per family in the sample will be between 0.8 and 1.0

Step-by-step explanation:

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

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

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

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

Mean 0.9 and standard deviation 1.1.

This means that [tex]\mu = 0.9, \sigma = 1.1[/tex]

Suppose a television network selects a random sample of 1000 families in the United States for a survey on TV viewing habits.

This means that [tex]n = 1000, s = \frac{1.1}{\sqrt{1000}} = 0.035[/tex]

a. Describe (as shape, center and spread) the sampling distribution of the possible values of the average number of children per family.

By the Central Limit Theorem, it has an approximately normal shape, with mean(center) 0.9 and standard deviation(spread) 0.035.

b. What average numbers of children are reasonably likely in the sample?

By the Empirical Rule, 95% of the sample is within 2 standard deviations of the mean, so:

0.9 - 2*0.035 = 0.83

0.9 + 2*0.035 =  0.97

Average numbers of children between 0.83 and 0.97 are reasonably likely in the sample.

c. What is the probability that the average number of children per family in the sample will be 0.8 or less?

This is the p-value of Z when X = 0.8. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.8 - 0.9}{0.035}[/tex]

[tex]Z = -2.86[/tex]

[tex]Z = -2.86[/tex] has a p-value of 0.0021

0.0021 = 0.21% probability that the average number of children per family in the sample will be 0.8 or less.

d. What is the probability that the average number of children per family in the sample will be between 0.8 and 1.0?

p-value of Z when X = 1 subtracted by the p-value of Z when X = 0.8.

X = 1

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{1 - 0.9}{0.035}[/tex]

[tex]Z = 2.86[/tex]

[tex]Z = 2.86[/tex] has a p-value of 0.9979

X = 0.8

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.8 - 0.9}{0.035}[/tex]

[tex]Z = -2.86[/tex]

[tex]Z = -2.86[/tex] has a p-value of 0.0021

0.9979 - 0.0021 = 0.9958

0.9958 = 99.58% probability that the average number of children per family in the sample will be between 0.8 and 1.0

Answer:

Direct variation

[tex]k = 2.5[/tex]

Step-by-step explanation:

Given

The attached table

Required

The type of variation

First, we check for direct variation using:

[tex]k = \frac{y}{x}[/tex]

Pick corresponding points on the table

[tex](x,y) = (-2,-5)[/tex]

So:

[tex]k = \frac{-5}{-2} = 2.5[/tex]

[tex](x,y) = (4,10)[/tex]

So:

[tex]k = \frac{10}{4} = 2.5[/tex]

[tex](x,y) = (6,15)[/tex]

So:

[tex]k = \frac{15}{6} = 2.5[/tex]

Hence, the table shows direct variation with [tex]k = 2.5[/tex]

Answer:

Step-by-step explanation:

[tex]h(t)=-16t^2+96t\\\\h(t)=-t(16t-96)[/tex]

[tex]96=2^5*3\\\\16=2^4\\\\h(t)=-t(2^5*3*t-2^4)=-2^4t(2^1*3*t-1)\\\\h(t)=-16t(6t-1)[/tex]

the b) part is easy do it!

9514 1404 393

Answer:

  1/3

Step-by-step explanation:

The slope of a line is the ratio of its "rise" to its "run." The "rise" is the change in vertical distance, and the "run" is the corresponding change in horizontal distance between two points on the line. The formula for the slope is ...

  [tex]m=\dfrac{y_2-y_1}{x_2-x_1}\qquad\text{where $(x_1,y_1)$ and $(x_2,y_2)$ are points on the line}[/tex]

In this problem, you are told the line passes through the origin, which is point (x, y) = (0, 0), and through point (6, 2). Using these coordinates in the slope formula gives ...

  [tex]m=\dfrac{2-0}{6-0}=\dfrac{2}{6}=\boxed{\dfrac{1}{3}}[/tex]

__

You may notice that when the line passes through the origin, the slope is simply the ratio y/x of any point on the line. Here, that ratio is 2/6 = 1/3.

_____

Additional comment

A line through the origin is the graph of a proportional relationship. That is, y is proportional to x. The slope of the line is the constant of proportionality. The equation of the line is ...

  y = kx . . . . . . where k is the constant of proportionality.

The line in this problem statement will have the equation ...

  y = (1/3)x

Answer:

C. m<c = 140°

Step-by-step explanation:

Let's analyse each of the given options:

A. m<a = 140° is TRUE

Rationale: angle a and 140° are vertical angles. Vertical angles are congruent.

B. m<b = 140° is TRUE.

Rationale: angle a and 140° are alternate interior angles. Alternate interior angles are congruent.

C. m<c = 140° is NOT TRUE.

Rationale: angle c and 140° are same side interior angles. Same side interior angles are supplementary.

D. m<d = 140° is TRUE.

Rationale: angle d and 140° are corresponding angles. Corresponding angles are congruent.

Answer:

x=9

Step-by-step explanation:

Answer:

By using a pair of compasses and a ruler you can draw all angles

Answer:

The answer is the third one below

Answer:

x = 3

y = 8

Step-by-step explanation:

In the given triangle FGH,

m∠F + m∠G + m∠H = 180° [Triangle sum theorem]

60° + 90° + m∠H = 180°

m∠H = 30°

If the given triangles FGH and TUV are congruent, their corresponding sides will be equal in measure.

m∠F = m∠T

7y + 4 = 60°

7y = 56

y = 8

GH ≅ UV

8x - 12 = 12

8x = 24

x = 3

Using the AAS congruence theorem, the values of x and y that show that both triangles are congruent are: x = 3 and y = 8.

According to the angle-angle-side congruence theorem (AAS), two triangles are congruent if they have two corresponding congruent angles and one pair of corresponding non-included sides that are congruent.

Thus, by the AAS theorem, we have:

8x - 12 = 12

8x = 12 + 12

8x = 24

x = 3

Also,

7y + 4 = 60

7y = 60 - 4

7y = 56

y = 8

Therefore, using the AAS congruence theorem, the values of x and y that show that both triangles are congruent are: x = 3 and y = 8.

Learn more about AAS congruence theorem on:

https://brainly.com/question/3168048

Answer:

This question seems incorrect.

Kindly take a look again and re-state it properly to enable me give the most accurate answer.

Thank you

Answer:

The slope is the cost per hour.

$5 per hour

Answer:

1437.3 cm^3 is the volume of sphere whose radius is 7cm

Answer:

(D.) 3x^2 + 6x

Step-by-step explanation:

the other options aren't complete and some don't even create a parabola.

Answer:

the answer is 50 but I don't know if

Answer:

E. by the SAS similarity theorem.

Step-by-step explanation:

Included angle x° in ∆ ABC ≅ included angle x° in ∆EDC (vertical angles are equal)

DC/BC = 240/150 = 1.6

EC/AC = 320/200 = 1.6

This implies that the ratio of two corresponding sides of both triangles are the same.

Two triangles are considered similar to each other by the SAS similarity theorem of they have a corresponding included angle that is equal and two corresponding sides that are congruent to each other. Therefore, both triangles are similar by the SAS similarity theorem.

Answer:

AB is perpendicular to [GH] and GH is [A]

Step-by-step explanation:

The freezing point of water is 0°C or 32°F while the boiling point of  water is 100°C or 212°F.

Temperature is the measure of the degree of hotness or coldness of a substance or place. It is usually expressed Fahrenheit and Celsius scale. Temperature indicates the direction of heat flow.

The freezing point of water is 0°C or 32°F while the boiling point of  water is 100°C or 212°F.

Find out more on Temperature at: https://brainly.com/question/24746268

Answer:

-192

Step-by-step explanation:

it is a geometric progression

r=-4

Answer:

v See below. v

Step-by-step explanation:

LM = MN

11x - 21 = 8x + 15

[tex]3x-21=15\\3x=36\\[/tex]

x = 12

LM = 11(12) - 21 = 132 - 21 = 111

MN = 8(12) + 15 = 96 + 15 = 111

LN = 111 + 111 = 222

Given:

Size of a red blood cell = 0.000007 m

Size of a plant cell = 0.0000127 m

To find:

The comparison of these two values.

Solution:

We have,

Size of a red blood cell = 0.000007 m

Size of a plant cell = 0.0000127 m

Clearly, [tex]0.0000127>0.000007[/tex]. Now, the difference between these two values is:

[tex]0.0000127-0.000007=0.0000057[/tex]

Therefore, the size of a plant cell is 0.0000057 m more than the size of a red blood cell.

Answer:

[tex]-2[/tex]

Step-by-step explanation:

Just substitute -3 for all instances of x.

[tex](-3)^{2} + 4(-3) + 1\\\\[/tex]

[tex]9 - 12 + 1[/tex]

[tex]-2[/tex]

Answer:

Step-by-step explanation:

Set this up as a proportion with the ratios being

[tex]\frac{vinegar}{oil}[/tex]  If there is a 2:5 ratio of vinegar to oil, that ratio looks like this:

[tex]\frac{v}{o}:\frac{2}{5}[/tex] and if we are looking for how much oil, x, is needed for 20 ml of vinegar, then that ratio completes the proportion:

[tex]\frac{v}{o}:\frac{2}{5}=\frac{20}{x}[/tex] and cross multiply.

2x = 100 so

x = 50 ml of oil

Answer:

F) Convenience Sampling

Step-by-step explanation:

Samples may be classified as:

Convenient: Sample drawn from a conveniently available pool.

Random: Basically, put all the options into a hat and drawn some of them.

Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.

Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.

Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.

A statistics student interviews the last fifteen attendees to arrive.

Conveniently available, so convenience, and the correct answer is given by option F.

Answer:

150 dollars. if I am wrong correct me

Answer:

C and D

Step-by-step explanation:

15 to 30 galons at $9.95 to $21.00

the minimum amount can be found by calculating the minimum amount sold at a minimum price 15*9.95 = $149.25

the maximum amount can be found by calculating the maximum amount sold at a maximum price 30*21 = $630

there are 2 choices that are between 149.25 and 630, C, and D

Answer:

4.32 = k

Step-by-step explanation:

8/k = 5/2.7

We can solve using cross products

8* 2.7 = 5k

21.6 = 5k

Divide each side by 5

21.6/5 = k

4.32 = k

Answer: 5k = 21.6 and k = 4.32

there you go have a good day bye

Step-by-step explanation:

Add boys and girls together for total students:

40 + 16 = 56 total students

Girls to total students is 16/56

Divide both numbers by 8 to get 2/7

The ratio is 2/7

[tex]\sf{\bold{\blue{\underline{\underline{Given}}}}}[/tex]

[tex]\sf{\bold{\red{\underline{\underline{To\:Find}}}}}[/tex]

[tex]\sf{\bold{\purple{\underline{\underline{Solution}}}}}[/tex]

In a class,

boys=40

girls =16

So,

The students of the class =

According to the question,

we have to find the ratio of girls to the total students

⠀⠀⠀⠀

[tex]\sf{\bold{\green{\underline{\underline{Answer}}}}}[/tex]

⠀⠀⠀⠀

Hence,the ratio of girls to students is 2:7

⠀⠀⠀⠀

Hello!

∫[(x+1)/(x-1)dx

∫t+2/t dt

∫t/t + 2/t dt

∫1 + 2/t dt

∫1dt + ∫2/t dt

∫t + 2In (|t|)

x - 1 + 2In (|x-1|)

x + 2In (|x-1|) + C, C ∈ R

Good luck! :)

Answer:

m = 4

n = 5

Step-by-step explanation:

[tex]m + 8 = 3m\\\\m - 3m = - 8\\\\-2m = - 8\\\\m = 4[/tex]

[tex]2n - 1 = 9 \\\\2n = 9 + 1\\\\2n = 10\\\\n = 5[/tex]

Answer:

The first one (90, 90) is supplimentary, the next two (54, 36. and 45, 45) are complimentary, and the last two are supplimentary.

Step-by-step explanation:

A complimentary angle is two angles that add up to 90, and supplimentary is two angles that add up to 180! :)

Answer:

1st picture at the top would be a supplementary angle because a supplementary angles always add to 180 degrees.

the 54 and 36 one is a complementary angle

the 45 and 45 would be complementary angle

the last two on the bottom would both be supplementary angles.

High hopes-

Barry