ADVANCED PLACEMENT AP MIDDLE SCHOOL

The distribution of random variable R has mean 10 and standard deviation 4. The distribution of random variable S has mean 7 and standard deviation 3. If R and S are independent, what are the mean and standard deviation of the distribution of R−S ?A) Mean 3 and standard deviation 1

B) Mean 3 and standard deviation 5

C) Mean 3 and standard deviation 7

D) Mean 17 and standard deviation 1

E) Mean 17 and standard deviation 5

Answers

Answer 1

Answer:

The mean and standard deviation of the distribution of R−S is;

Option B; Mean 3 and standard deviation 5

We are given details of two random variables R and S.

RandomVariableR;

- Mean; μ_R = 10

- Standard deviation; σ_R = 4

RandomVariable S;

- Mean; μ_S = 7

- Standard Deviation; σ_S = 3

We want to carry out R - S for both mean and standard deviation

1) For Mean; R - S would simply be done by subtracting normally as done in arithmetic operations.

Thus; μ_R - μ_S = 10 - 3

μ_R - μ_S = 7

2) For standard deviation;

We know that standard deviation is not independent as it is the square root of variance.

Therefore, if we want to add or subtract standard deviations, it means that the variation will increase.

Thus, the difference in standard deviation is;

σ_R - σ_S = √((σ_R)² + (σ_S)²)

σ_R - σ_S = √((4)² + (3)²)

σ_R - σ_S = √25

σ_R - σ_S = 5

In conclusion, the distribution of R - S gives;

Mean = 3 and Standard deviation = 5

Read more at; brainly.com/question/2800112

Answer 2

Answer:

Answer: B

Mean of 3 and Standard deviation of 5

Explanation:

Performing operations on means of independent variables is similar to performing arithmetic operations on natural numbers.

Subtracting the mean of S from R is 10 - 7 = 3

For the difference in standard deviation. It should be noted that when combining variables, the variation within the distribution. So therefore, adding or subtraction of variables, the variation will increase and will yield same answer.

To obtain the difference in standard deviation, the variances of the random variables has to be added and then the square root will be taken to return back to standard deviation.

SD(R-S)=sqrt(R²+S²)

SD=sqrt(4²+3³)

SD=sqrt(25)

SD=5

Related Questions

Which system is used to measure physical properties? its for forensics
Describe King Hrothgar. Does he fit the expectation of anAnglo-Saxon king?
Pigment does what to paint?
Which sentence is written in third-person point of view?a Once a small crowd of protesters, we were now an angry mob. b Our small crowd of protesters was now an angry mob. c The small crowd of protesters had turned into an angry mob. d Your small crowd of protesters has now become an angry mob.
analyze the economic development during the twentieth century in Sub-saharan Africa, Southeast asia, or the middle east.(pick one region)#one paragraph is all i need

Identify what types of government services need to be provided in a city with an increasing old-age dependency

Answers

Answer:

Down below

Hope it helped

The government needs to provides more health care centers and health insurance. They can provide old age pensions and homes, as well as other welfare measures.

During What Period Of Music Does The Rondo Form Become Popular?1. renaissance
2. Baroque
3. Impressionist

Answers

The answer is 3. Impressionist

I think it’s Renaissance but impressionist might be right

What do you think when you see this image? What do you think it represents?

Answers

i personally see a desert with foot steps that left i think it would represent lonleyness or the act of abandoning something perhaps what used to be a city

Answer:

it means abandoning

Explanation:

he/she left the cart behind

melinda rode her bike 54/100 mile to the library then she rode 4/10 mile to the store how far did melinda ride her bike in all

Answers

4/10 is the equivalent of 40/100. Add that to 54/100 and the answer is 94/100

Alright. We are looking for total distance so let's start with saying we must add. To find a common denominator multiply the term (4/10) by 10. Now we have 54/100 + 40/100. This equals 94/100 which can be reduced to 47/50 miles.

Which of the following statements best predicts the effect of increasing the permeability of the mitochondrial membranes to large molecules?

Answers

The options missing from the question is given below:

ATP production will increase because of an increase in the rate at which proteins diffuse out of mitochondria;
ATP production will increase because of an increase in the mixing of mitochondrial and cytosolic substances;
ATP production will decrease because of an increase in the occurrence of uncontrolled chemical reactions;
ATP production will decrease because of an increase in the surface area of the mitochondrial membranes

The correct answer is 3 above.

ATP production reduces and ultimately drops due to the irregularities caused by the increased permeability of the mitochondrial membranes.

Also triggered by the increase in permeability are bioenergetic crises and a decrease in oxygen consumption rate.

Osmotic imbalance and changes in the ion homeostasis of the cell-matrix is the major causative factor for Mitochondrial swelling.

Learn more about Mitochondrial Membranes in the link below:

brainly.com/question/1602075

Weight and mass are related but different properties. If the mass of Earth were to double, the mass of an object on Earth would remain the same. What change would we expect to see in the weight of an object?A.The weight would decrease by 100
B.The weight would be reduced by half?
C.The weight would double.
D.The weight would increase four times.

Answers

i believe it’s c) the weight would double, but i’m not 1000% positive

C is the correct answer

Explanation:
Doubling the mass of the Earth would double your weight, since gravitational force is directly proportional to mass, but doubling the radius (which doubles if the diameter doubles) would decrease your weight by a factor of 1/4, since gravitational force is inversely proportional to the square of the radius

Other Questions

Which sentence is true about preconception care?A. Women who are thinking about having a child should not worry about preconception care as it is unnecessary. B. Preconception care is health care you receive after you get pregnant.C. It is aimed at finding and taking care of problems that could affect you or the baby during pregnancy and steps to reduce birth defects. D. It will involve taking medication and a strict diet and exercise plan.

What personal touches can you add to your outlines which make creating and studying from them easier?

Select the correct answer. A buyer from a furniture company wants to buy foam for production purposes. The buyer decides to purchase it from the same supplier used by the company in the previous year. What kind of buying situation does this represent? A. new task B. straight rebuy C. modified rebuy D. indirect rebuy

Mr. Fuller assigned his science class a lab comparing the masses of objects to the nearest gram using a balance. The mass of a paper clip is about 1 gram. How many paper clips will it take to balance the scale, if it is determined that a 1 centimeter cube of gold has the mass of 19.3 grams?