Let X be a continuous random variable with PDF 2x 0

a) Only the first statement is true. As the sample size N becomes large, the sample mean of IID random samples from a population becomes more precise and approaches the true population mean.

However, there is no direct relationship between the sample size and the distribution of the sample mean.
The second statement is only true if the population is normally distributed. If the population is not normal, the distribution of the sample mean may not be normal, and the central limit theorem may not apply. Therefore, option c) is not the correct answer. Option d) is also not correct as the first statement is true.

To learn more about mean visit;

brainly.com/question/31101410

#SPJ11

To communicate information about the public in broadly understandable terms, researchers and pollsters often rely on aggregated statistical data. By compiling and analyzing large sets of information, they can identify patterns and trends that can be presented in a way that is easy for people to understand.

For example, they may use graphs, charts, or other visual aids to convey complex information in a clear and concise manner. This can be particularly important when trying to share findings with the general public or with policymakers who may not have a background in statistics or research methodology. By using aggregated statistical data, researchers and pollsters can help ensure that important information is communicated effectively and accurately.

This allows them to present complex information in a more accessible and easily digestible format for a wider audience.

To learn more about pollsters : brainly.com/question/2729655

#SPJ11

An interesting relationship in the population may fail to achieve statistical significance if there are too few observations or sample size is too small.

Statistical significance is a measure of the probability that the observed relationship between variables in a sample could have occurred by chance alone. When a relationship is statistically significant, it means that the probability of observing the relationship by chance is very low, typically less than 5% (p < 0.05).

However, if the sample size is too small, there may not be enough data to detect a real relationship between variables, even if it exists in the population. In such cases, the observed relationship may not be statistically significant, even though it is important and meaningful.

Increasing the sample size can help to increase the power of the analysis, making it more likely to detect a true relationship between variables. Thus, having a sufficiently large sample size is important for achieving statistical significance and for making reliable conclusions about the relationship between variables.

learn about Statistical significance,

https://brainly.com/question/15848236

#SPJ11

Each guy-wire is approximately 315.08 feet long.

We can use trigonometry to find the length of the guy-wires. Let's call the length of each guy-wire "x".

First, we can use the tangent function to find the height of the triangle formed by the first guy-wire and the antenna:

tan(0.33) = height/x

Rearranging, we get:

height = x * tan(0.33)

Similarly, we can use the tangent function to find the height of the triangle formed by the second guy-wire and the antenna:

tan(0.38) = height/x

Again, rearranging, we get:

height = x * tan(0.38)

Since both of these triangles share the same height, we can set the two expressions for height equal to each other:

x * tan(0.33) = x * tan(0.38)

Dividing both sides by x gives:

tan(0.33) = tan(0.38)

This equation is not true for all values of alpha and beta, but we are given that it holds for this particular case. Using this equation, we can solve for x:

x = 160 / tan(0.33)

x ≈ 315.08 feet

Therefore, each guy-wire is approximately 315.08 feet long.

To learn more about equation visit:

https://brainly.com/question/29657983

#SPJ11

The area to the right of z = -2.71 and the area to the right of z = 2.71 under the standard normal curve are both approximately 0.0034.

To find the area under the standard normal curve to the right of z = -2.71, we need to calculate the area between z = -2.71 and z = infinity. This can be done using a standard normal distribution table or calculator, which will give us an area of approximately 0.0034.

To find the area under the standard normal curve to the right of z = 2.71, we can use the same approach but this time we need to calculate the area between z = 2.71 and z = infinity. Again, using a standard normal distribution table or calculator, we can find this area to be approximately 0.0034.

Know more about standard normal curve here:

https://brainly.com/question/28971164

#SPJ11

Answer:

19

Step-by-step explanation:

Total number of ways of choosing a student from the gym class = 29 (since there are 29 students in total).

Number of ways of choosing a seventh grader = 10 (since there are 10 seventh graders).

Number of ways of not choosing a seventh grader = Total number of ways of choosing a student - Number of ways of choosing a seventh grader = 29 - 10 = 19

The decision and outcome that represents a Type I error in this scenario is if the prisoner is released and kills a family of five in cold blood within 48 hours. A Type I error occurs when the null hypothesis is rejected even though it is actually true. In this case, if the parole board releases the prisoner based on the hypothesis that they have been rehabilitated but in reality, they have not been rehabilitated, it would result in a Type I error. The prisoner's release would lead to a tragic outcome, which could have been avoided if the null hypothesis had not been rejected.

Learn more about Type I error here:

https://brainly.com/question/24320889

#SPJ11

Probability is the likelihood or chance of an event occurring.

In the given grid, there are 4 black points out of a total of 9 points.

Therefore, the probability of selecting a black point randomly is:

P(black) = Number of black points / Total number of points

= 4 / 9

= 0.444 or 44.4% (rounded to one decimal place)

learn about probability,

https://brainly.com/question/13604758

#SPJ11

The correct expression for the estimated model is: In (odds ratio) = -7.8562 +0.0304 Income + 1.2804 Lawnsize. This model was created using binary logistic regression analysis to study the characteristics that differentiate home owners who have a lawn service (code 1) and those who do not (code 0).

The additional information available for these 30 home owners includes family income (Income, in thousands of dollars) and lawn size (Lawn Size, in thousands of square feet). The estimated model shows that for every one unit increase in income,

the odds of having a lawn service increase by 0.0304, and for every one unit increase in lawn size, the odds of having a lawn service increase by 1.2804. This information can be useful for the marketing manager to target potential customers based on their family income and lawn size.
The correct expression for the estimated model in this case is:

ln(odds ratio) = -7.8562 + 0.0304 Income + 1.2804 Lawn Size

Learn more about ratio here:- brainly.com/question/13419413.

#SPJ11

The expression  3 / 4 a + 8 - 1 / 4 a - 2  is equivalent to  1 / 2(a + 12)..

'

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

The equivalent expression can be found by simplifying the expression as follows:

Therefore,

3 / 4 a + 8 - 1 / 4 a - 2

collect like terms

3 / 4 a  - 1 / 4 a + 8 - 2

3a - 1a / 4 + 6

2a/ 4 + 6

1 / 2 a + 6

Therefore, the second expression is 1 / 2(a + 12).

Let's open the brackets

1 / 2(a + 12) = 1 / 2a + 6

Therefore, the expression are equivalent.

learn more on equivalent expression here: brainly.com/question/16609931

#SPJ1

There are several subtypes of qualitative data techniques, including interview, focus groups, observations, case studies and document analysis.

Interviews: These are one-on-one conversations between the researcher and participant(s), where the researcher asks open-ended questions to gather information.

Focus Groups: These are group discussions where a researcher moderates the conversation and asks participants to share their experiences and opinions on a particular topic.

Observations: These involve the researcher directly observing and documenting behaviors, actions, and interactions of individuals or groups in a natural setting.

Case Studies: These involve in-depth exploration and analysis of a single individual or group, often used in fields such as psychology and social work.

Document Analysis: This involves reviewing and analyzing written or recorded materials such as texts, videos, or audio recordings to gain insight into a particular topic or phenomenon.

More on qualitative data: https://brainly.com/question/10926775

#SPJ11

a. The scatter diagram for these data with the speed of execution as the independent variable would plot each brokerage firm's speed of execution score on the x-axis and their overall satisfaction rating score on the y-axis.

b. The scatter diagram developed in part (a) shows a positive correlation between the speed of execution and overall satisfaction rating. As the speed of execution score increases, the overall satisfaction rating score also tends to increase.

c. The least squares estimated regression equation is:

y = 2.108 + 0.473x

where y represents the overall satisfaction rating score and x represents the speed of execution score.

d. The slope of the estimated regression equation (0.473) represents the change in the overall satisfaction rating score for a one-unit increase in the speed of execution score. In other words, on average, for every increase of 1 in the speed of execution score, the overall satisfaction rating score is predicted to increase by 0.473.

e. If Zecco.com's speed of execution rating increased from 2.7 to the average speed of execution rating (3.3), we can use the estimated regression equation to predict their new overall satisfaction rating score:

y = 2.108 + 0.473(3.3) = 3.616

Therefore, we would predict a new overall satisfaction rating score of approximately 3.616 for Zecco.com if they increased their speed of execution rating to the average of the other 10 brokerage firms surveyed.

Learn more about scatter diagram here:

https://brainly.com/question/31102167

#SPJ11

The APR (annual percentage rate) for a $2,000 loan paid off in 12 equal monthly payments with a stated annual interest rate of 8% is 14.452%.

The annual percentage rate (APR) can be determined using an online finance calculator as follows:

The APR is the total cost of borrowing money, reflecting not only the interest rate but also other loan fees.

N (# of periods) = 12 months

PV (Present Value) = $2,000

PMT (Periodic Payment) = $-180

FV (Future Value) = $-0

Results:

I/Y = 14.452% if interest compounds 12 times per year (APR)

I/Y = 15.449% if interest compounds once per year (APY)

I/period = 1.204% interest per period

Sum of all periodic payments = $-2,160.00 ($180 x 12)

Total Interest = $160.00 ($2,000 x 8%)

Learn more about the annual percentage rate (APR) at https://brainly.com/question/2772156.

#SPJ1

The correct prime numbers x that make this inequality true is,

⇒ x = 7, 11, 13, 17, 19

We have to given that;

The expression is,

''5 is less than x and x is less than or equal to 19.''

Now, We can formulate;

⇒ 5 < x ≤ 19

Hence, Possible prime numbers that make this inequality true are,

⇒ x = 7, 11, 13, 17, 19

Thus, The correct prime numbers x that make this inequality true is,

⇒ x = 7, 11, 13, 17, 19

Learn more about the inequality visit:

https://brainly.com/question/25944814

#SPJ5

The ordinary number form of the mentioned scientific notation form of the number is 0.00604.

Scientific notation of representation of a number refers to converting a number to its readable form. It is applicable on both small and large numbers, where value of zeroes are represented in exponential form for easy interpretation.

The exponent of -3 is interpreted as three zeroes in the denominator. The division with zero will further shorten the number by adding zeroes to left hand side of the digit after decimal. Hence, the ordinary form of the number will be 0.00604.

Learn more about scientific notation -

https://brainly.com/question/1767229

#SPJ4

To determine how far a cheetah could run in 15 seconds at the given rate, we can use the formula:

distance = rate x time

Where the rate is the speed at which the cheetah is running and time is the duration of the run.

We are given that the cheetah runs 420 feet in 6 seconds. To find the rate at which the cheetah is running, we can divide the distance by the time:

Now we can use the rate and the given time of 15 seconds to find the distance the cheetah could run:

Therefore, the cheetah can run 1050 feet in 15 seconds.

The bottom of the ladder is sliding along the ground away from the wall at a rate of 25/12 ft/s when it is 12 feet away from the base of the wall.

Let's denote the height of the ladder on the wall as y, and the distance of the ladder's bottom from the wall as x. We know that y and x are related by the Pythagorean theorem: [tex]x^2 + y^2 = 13^2.[/tex]

We are given that dy/dt = -5 ft/s (the negative sign indicates that the ladder is slipping down the wall) and we want to find dx/dt when x = 12 ft.

To solve for dx/dt, we need to relate x and y, and then differentiate with respect to time:

[tex]x^2 + y^2 = 13^2[/tex]

Differentiating both sides with respect to time t:

2x(dx/dt) + 2y(dy/dt) = 0

When x = 12 ft, we can solve for y using the Pythagorean theorem: y = sqrt[tex](13^2 - 12^2)[/tex] = 5 ft.

Substituting x = 12 ft and dy/dt = -5 ft/s into the above equation, we get:

2(12)(dx/dt) + 2(5)(-5) = 0

Simplifying and solving for dx/dt, we get:

dx/dt = 25/12 ft/s

Therefore, the bottom of the ladder is sliding along the ground away from the wall at a rate of 25/12 ft/s when it is 12 feet away from the base of the wall.

Learn more about ladder

brainly.com/question/28636911

#SPJ11

The object will be at the height of 78.4 meters after 2 seconds after substituting to the equation.

Given that,

An object is launched at 19.6 meters per second (m/s) from a 58.8-meter tall platform.

The equation for the object's height s at time t seconds after launch is,

s(t) = -4.9t² + 19.6t + 58.8

where s is in meters.

We have to find the height of the object after 2 seconds.

When t = 2,

s = (-4.9 × 4) + (19.6 × 2) + 58.8

s = -19.6 + 39.2 + 58.8

s = 78.4 meters

Hence the height of the object after 2 seconds is 78.4 meters.

Learn more about Equations here :

https://brainly.com/question/30302823

#SPJ1

the tradeoff between x and y is such that the weighted sum of their square roots is constant.

To derive the equation for the indifference curve, we need to find the combinations of x and y that yield the same level of utility U. Mathematically, we can express this as:

U(x, y) = constant

Substituting the given utility function, we get:

(.6x.5 + .4y.5)1/.5 = constant

Simplifying, we get:

(.36x + .16y) = constant^2

Dividing by the constant squared, we get:

(.36x + .16y)/constant^2 = 1

This is the equation for the indifference curve, which represents all the combinations of x and y that yield the same level of utility U. The constant represents the level of utility, and the equation shows that the tradeoff between x and y is such that the weighted sum of their square roots is constant.

learn about utility function,

https://brainly.com/question/31498128,

#SPJ11

The Empirical Rule is a statistical principle that applies to normally distributed data. It states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% of the data falls within two standard deviations of the mean, and 99.7% of the data falls within three standard deviations of the mean.

In this case, the mean triglyceride level for the residents of the assisted living facility is 200, with a standard deviation of 50. If samples of 100 residents are taken, the sample mean triglyceride level will also be normally distributed, with a mean of 200 and a standard deviation of 5 (calculated as 50 divided by the square root of 100).

To find the range within which 95% of all the sample means will fall, we need to look at two standard deviations above and below the mean. Two standard deviations above the mean are 210 (calculated as 200 + 2*50), and two standard deviations below the mean are 190 (calculated as 200 - 2*50).

Therefore, we can conclude that 95% of all sample means will fall between 190 and 210. So the lower value is 190, and the upper value is 210.

Learn more about  Empirical Rule here:

https://brainly.com/question/30700783

#SPJ11

The tabled value for a x^2 variable based on 50 degrees of freedom with an area of 0.025 to its right is x² = 69.34 (rounded to two decimal places).

To find the tabled value for a x^2 variable based on n-1 degrees of freedom with an area of a to its right, we need to use a chi-square distribution table.

For this problem, n = 51 and a = 0.025. First, we need to find the degrees of freedom. Since we are using a x^2 variable, the degrees of freedom is n - 1 = 51 - 1 = 50.

Next, we need to find the critical value from the chi-square distribution table with 50 degrees of freedom and an area of 0.025 to its right.

From the table, we find that the critical value is 69.338.

Learn more about chi-square distribution table here:

https://brainly.com/question/30764634

#SPJ11

Answer:

The answer for

<H=41°

<F=49°

Step-by-step explanation:

sum of angles in a triangle equals 180°

90+2x+35+3x+20=180

C.L.T.

2x+3x+90+20+35=180

5x+145=180

5x=180-145

5x=35

divide both sides by 5

5x/5=35/5

x=7

so<H=3(7)+20=21+20=41°

<F=2(7)+35=14+35=49°

If events A and B are independent, then P(B|A) = P(B).

From the given information, we have:

P(B|A) = 0.32

P(A) = 0.54

Using the formula for conditional probability, we can write:

P(B|A) = P(A and B) / P(A)

Solving for P(A and B), we get:

P(A and B) = P(B|A) x P(A) = 0.32 x 0.54 = 0.1728

Now, to find P(B), we can use the formula:

P(B) = P(B and not A) + P(B and A)

Since A and B are independent, we have:

P(B and not A) = P(B) - P(A and B) = P(B) - 0.1728

Substituting the given values, we get:

P(B) - 0.1728 + 0.1728 = 0.33

P(B) = 0.33 + 0.1728 = 0.5028

Therefore, the probability of event B is 0.5028

learn about probability,

https://brainly.com/question/13604758

#SPJ11

The probability of selecting a user who chooses cinnamon and is under 13 years old is: 0.18 or 18% (rounded to two decimal places).

In the problem, we are given the number of users who choose bacon and are under 13 years old, which is 8. We are also given the number of users who choose plain and are under 13 years old, which is 5. Therefore, the total number of users under 13 years old is 8 + 5 = 13.

Next, we are asked to find the probability of selecting a user who chooses cinnamon and is under 13 years old. We know that the number of users who choose cinnamon and are under 13 years old is 3. Therefore, out of the total 13 users under 13 years old, the probability of selecting a user who chooses cinnamon and is under 13 years old is:

The total number of users under 13 years old is 8 (choose bacon) + 5 (choose plain) = 13.

The number of users who choose cinnamon and are under 13 years old is 3.

Therefore, the probability of selecting a user who chooses cinnamon and is under 13 years old is:

3 / 13 ≈ 0.23 or 23% (rounded to two decimal places)

To know more about probability,

https://brainly.com/question/30034780

#SPJ11

In descriptive statistics, the interquartile range tells you the spread of the middle half of your distribution. Quartiles segment any distribution that's ordered from low to high into four equal parts. The interquartile range (IQR) contains the second and third quartiles, or the middle half of your data set.

Answer:

WHere is the question

Step-by-step explanation:

The equation of the graph is y = -| x | + 1

Given data ,

The graph of y = -|x| + 1 is a V-shaped graph with the vertex at the origin (0, 1), and it opens downwards along the y-axis. The negative sign in front of the absolute value function reflects the graph of y = |x| across the x-axis, flipping it upside down.

When x is greater than or equal to 0, the expression |x| becomes x, and the graph of y = -|x| + 1 will be y = -x + 1 for x ≥ 0.

When x is less than 0, the expression |x| becomes -x, and the graph of y = -|x| + 1 will be y = x + 1 for x < 0.

Thus, the graph of y = -|x| + 1 consists of two linear segments with slopes of -1, intersecting at the point (0, 1), and extends indefinitely in both directions along the x-axis.

Hence , the equation of graph is y = -| x | + 1

To learn more about equation of graph of polynomials click :

https://brainly.com/question/16957172

#SPJ1

y=-|x|+1

Step-by-step explanation:

I checked RSM, its correct

We are given two sets of paired observations, which we will use to calculate the sample mean difference and the standard error of the mean difference:

Sample mean difference = x1 -x2 = (214+186+182+200+210+204+187+210+190+182+215+198)/12 - (188+210+199+209+207+195+203+191+190+211+199+181)/12 = 4.75

Sample standard deviation of the differences = s = √[(Σd²)/(n-1)] where d = (x1 - x2) - (x1 - x2), and n is the number of pairs.

d1 = (214 - 188) - 4.75 = 21.25

d2 = (186 - 210) - 4.75 = -28.75

d3 = (182 - 199) - 4.75 = -22.75

d4 = (200 - 209) - 4.75 = -9.75

d5 = (210 - 207) - 4.75 = -1.75

d6 = (204 - 195) - 4.75 = 3.25

d7 = (187 - 203) - 4.75 = -20.75

d8 = (210 - 191) - 4.75 = 13.25

d9 = (190 - 190) - 4.75 = -4.75

d10 = (182 - 211) - 4.75 = -28.75

d11 = (215 - 199) - 4.75 = 10.25

d12 = (198 - 181) - 4.75 = 12.25

Σd² = 1734.875

s = √(1734.875/11) = 5.076

Standard error of the mean difference = s/√n = 5.076/√12 = 1.469

Using a t-distribution with 11 degrees of freedom and a 99% confidence level (α = 0.01), we find the t-value to be 3.106. Therefore, the 99% confidence interval for the true mean difference between the cholesterol levels for people who take the new drug is:

(4.75 - 3.106(1.469), 4.75 + 3.106(1.469))

= (0.885, 8.615)

So we are 99% confident that the true mean difference between the cholesterol levels for people who take the new drug lies between 0.885 and 8.615 mg/dL.

Visit here to learn more about mean brainly.com/question/31101410

#SPJ11

The value of the coordinates of the points R’, S’ and T’ are,

R' = (1, - 2)

S' = (- 8, 2)

T' = (- 4, 7)

We have to given that;

ΔRST is reflected across the line y=x to form ΔR'S'T'.

Here, All the coordinates are,

R = (- 2, 1)

S = (2, - 8)

T = (7, - 4)

Hence, After reflection across y = x, the coordinates of the points R’, S’ and T’ are,

R' = (1, - 2)

S' = (- 8, 2)

T' = (- 4, 7)

Thus, The value of the coordinates of the points R’, S’ and T’ are,

R' = (1, - 2)

S' = (- 8, 2)

T' = (- 4, 7)

Learn more about the transformation visit:

https://brainly.com/question/30097107

#SPJ1