8. Daren and Josh are pretty good free throw shooters. Daren makes 75% of the
free throws he attempts. Josh makes 80% of his free throws. Suppose we take
separate random samples of 50 free throws each from Daren and Josh, and
record the proportion of free throws that are made by each. Which of the
following best describes the sampling distribution of PD - Pj?
Answers
Answer:
B) Approximately normal, with mean -0.05 and standard deviation 0.083
Step-by-step explanation:
The correct answer is (B). The shape is approximately normal since the expected number of makes and misses for both Daren and Josh are all greater than 10.
The distribution of pD = pJ is given by: Option B: Approximately normal, with mean -0.05 and standard deviation 0.083
What is the distribution of population proportion?For large enough sample, let the population proportion of a quantity be denoted by random variable \(p\)
Then, we get:
\(p \sim N(\hat{p}, \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}})\)
where
\(\hat{p}\) = estimated(mean value) proportion of that quantity, and n = size of sample drawn.What is the distribution of random variable which is sum of normal distributions?
Suppose that a random variable X is formed by n mutually independent and normally distributed random variables such that:
\(X_i = N(\mu_i , \sigma^2_i) ; \: i = 1,2, \cdots, n\)
And if
\(X = X_1 + X_2 + \cdots + X_n\)
Then, its distribution is given as:
\(X \sim N(\mu_1 + \mu_2 + \cdots + \mu_n, \: \: \sigma^2_1 + \sigma^2_2 + \cdots + \sigma^2_n)\)
Here, we're specified that:
For proportion of correct free throw attempts by Daren:
Sample size = n = 50Estimated proportion = \(\hat{p}_D = 75\% = 0.75\)Let the population proportion be represented by variable \(p_D\)For proportion of correct free throw attempts by Josh:
Sample size = n = 50Estimated proportion = \(\hat{p}_J = 80\% = 0.8\)Let the population proportion be represented by variable \(p_J\)And therefore, we have:
\(p_D \sim N\left (0.75, \sqrt{\dfrac{0.75 \times 0.25}{50}}\right )\\\\p_J \sim N\left (0.80, \sqrt{\dfrac{0.8 \times 0.2}{50}}\right )\)
And therefore, we get:
\(-p_J \sim N\left (-0.80, \sqrt{\dfrac{0.8 \times 0.2}{50}}\right )\) (standard deviation doesn't get affected by change of sign of the considered random variable, and mean gets affected linearly, so mean became negative 0.80 and standard deviation stays same).
Adding \(p_D\) and \(-p_J\), we get:
\(p_D + (-p_J) = p_D - p_j \sim N\left (0.75 -0.80, \sqrt{\dfrac{0.8 \times 0.2}{50} + \dfrac{0.75 \times 0.25}{50}}\right )\\\\p_D - p_J \sim N\left( -0.05, 0.0837\right)\)
Thus, the distribution of pD = pJ is given by: Option B: Approximately normal, with mean -0.05 and standard deviation 0.083
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Related Questions
How many roots do the functions have in common f(x)=x^2+x-6
Answers
To find the common roots between two functions, we need to find the roots (or solutions) of each function individually and then identify the shared solutions.
For the function f(x) = x^2 + x - 6, we can find the roots by setting the function equal to zero and solving for x:
x^2 + x - 6 = 0
To factorize this quadratic equation, we need to find two numbers that multiply to -6 and add up to 1 (the coefficient of x). The numbers that satisfy these conditions are 3 and -2:
(x + 3)(x - 2) = 0
Setting each factor equal to zero:
x + 3 = 0 or x - 2 = 0
Solving for x in each equation:
x = -3 or x = 2
Therefore, the function f(x) = x^2 + x - 6 has two roots: x = -3 and x = 2.
To find the common roots between this function and another function, we would need to know the second function. If you provide the second function, I can help determine if there are any shared roots.
Cassie started with $48 in her savings account. She adds the same amount of money to the account each week. The table shows how much money
she has in her savings account at the end of each week shown. How much money does Cassie add to her savings account each week? Help ASAP
Answers
Answer:
I think its 12
Step-by-step explanation:
If you subtract from each its 36 but since it goes by 3 weeks you divide 36 by 3 and get 12. I am not 100% sure though.
Between x = 0 and x = 1, which function has a greater average rate of change than y = 3x
?
Answers
Answer:
x=1
Step-by-step explanation:
y=3x so just add 1+3=4 then add veriable y=4x
Solve 3^5x=10
HELP PLS
Answers
Answer:
x = 10/243
Step-by-step explanation:
3^5x = 10
243x = 10
Divide 243 on both sides
10/243
Joe wants to rent a scooter for a day. It will cost the daily fee of $15 plus $0.25 per mile driven. Let m = the number of miles Joe drives for the day. Write an expression that shows the amount he will pay for the car?
Evaluate the expression you wrote to find Joe will pay if he drives 20 miles?
Answers
Answer:
What you´re going to do, is 0.25 x 20, and that is about 5.00. Then you do 15 + 5 and you get 20 dollars for 20 miles. M = $20
Step-by-step explanation:
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
Answer:
100°
Step-by-step explanation:
tThe sum of all arc measures that make up that circle is 360 degrees.
QS + RQ + RS = 360
QS = 360 - 120 - 140 = 100
An arc angle is the degree measurement of that angle inside the circle, opposite the arc
m∠R = arc QS = 100°
Answer:
∠ R = 50°
Step-by-step explanation:
the inscribed angle R is half the measure of its intercepted arc QS
the sum of the arcs on a circle is 360° , that is
RQ + QS + SR = 360°
120° + QS + 140° = 360°
QS + 260° = 360° ( subtract 260° from both sides )
QS = 100°
Then
∠ R = \(\frac{1}{2}\) × 100° = 50°
n
2016
20162016, the city of Rio de Janeiro had a population density of
5377
people
km
2
5377
km
2
people
5377, start fraction, start text, p, e, o, p, l, e, end text, divided by, start text, k, m, end text, squared, end fraction .
What was the population density of Rio de Janeiro in people per square meter?
Answers
The population density of Rio de Janeiro in people per square meter is 5. 377 x 10 ⁻³ people per m²
How to find the population density ?To find the population density in meters squared when given the population density in kilometers squared, you first need to find the conversion factor between kilometer squared and meters squared.
1 kilometer squared is equal to 1, 000, 000 meters squared.
The population density of Rio de Janeiro in meters squared is therefore:
= Population density in kilometers squared / Conversion factor
= 5, 377 / 1, 000, 000
= 0. 005377
= 5. 377 x 10 ⁻³ people per m²
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The full question is:
In 2016, the city of Rio de Janeiro had a population density of 5377 people/km2.
What was the population density of Rio in people per square meter?
Please help with all I will mark brainly
Answers
Answer:
3. 33.33, 4. 43, 5. 31
Step-by-step explanation:
3. 60+40=100/3= 33.33
4. 85+1/2=86/2= 43
5. 100+86=186/6= 31
There are 37 oak Trees Correctly in the park park workers will Plant 27 more oak Trees today how many oak Trees will The park have when The workers are finished
Answers
Answer:
64
Step-by-step explanation:
37+27=64
Type the correct answer in each box. Functions h and K are inverse functions, and both are defined for all real numbers Using this relationship, what is the value of each function composition?
(h o k) (3)=
(k o h)(-4b) =
Answers
Answer:
(h o k) (3) = 3
(k o h) (-4b) = -4b
Step-by-step explanation:
An inverse function is the opposite of a function. An easy way to find inverse functions is to treat the evaluator like another variable, then solve for the input variable in terms of the evaluator. One property of inverse functions is that when one finds the composition of inverse functions, the result is the input value, no matter the order in which one uses the functions in the combination. This is because all terms in a function and their inverse cancel each other and the result is the input. Thus, when one multiplies two functions that are inverse of each other, no matter the input, the output will always be the input value.
This holds true in this case, it is given that (h) and (k) are inverses. While one is not given the actual function, one knows that the composition of the functions (h) and (k) will result in the input variable. Therefore, even though different numbers are being evaluated in the composition, the output will always be the input.
There is a circular pool in the backyard with an approximate area of 113 square inches. What was the diameter?
A.12 inches
B.36 inches
C.48 inches
D.144 inches
Answers
A circle is a curve sketched out by a point moving in a plane. The diameter of the circular poll is 12 inches. Thus, the correct option is A.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
The area of a circle is given as πR², where r is the radius of the circle. Since the area of the pool is 113 sq. inches, therefore, the radius of the circle will be,
Area of pool = πR²
113 sq. inches. = πR²
113/π = R²
R = √35.9690
R = 5.9974 ≈ 6 inches
Now, since the diameter of a circle is twice the radius of the circle, therefore, the diameter of the circle will be,
Diameter of the circle = 2 × 6 inches = 12 inches
Hence, the diameter of the circular poll is 12 inches. Thus, the correct option is A.
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Answer:
a. 12 inches
Step-by-step explanation:
113 ÷ 3.14 = 35.98726114649682
2√35.98726114649682 = 5.998938334947011
5.998938334947011 x 2 = 11.99787666989402
keyword approximate ;)
what answer? here, can you answer that? thankyou
Answers
It should be noted that the number of sample size based on the information will be 300.
How to explain the sampleIn order to calculate the sample size, we can use the following formula:
n = z² * p * (1-p) / E²
n = 1.96² * 0.5 * (1-0.5) / 0.05²
= 300
A questionnaire is a method of gathering data that makes use of written questions to be answered by the respondents. It is a popular method of data collection because it is relatively easy to administer and can be used to collect a wide variety of information.
In the first column, the population is the entire National Capital Region (NCR). The sample is the city of Manila. In the second column, the population is all STEM students. The sample is all academic track students. In the third column, the population is all the tablespoons of sugar in the jar. The sample is one tablespoon of sugar. In the fourth column, the population is all the vowels in the word "juice". The sample is the vowel "i".
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A rectangle has perimeter 88 cm and length 35 cm. What is its width?
Answers
Answer:
9
Step-by-step explanation:
35 plus 35 equals 70 and 9 plus 9 equals 18
A box is filled with 5red crayons, 9blue crayons, and 6yellow crayons.
A crayon is chosen at random from the box. Find the probability that it is a red or a blue crayon.
Write your answer as a fraction in the simplest form.
Answers
Answer:
\(\frac{7}{10}\)
Step-by-step explanation:
P(R or B)=\(\frac{5}{20}+\frac{9}{20}\)
=\(\frac{7}{10}\)
A pool measures 14 feet by 25 feet and it is surrounded by a -foot deck. How much fencing is needed to fence the outside of the deck?
Answers
Answer:
Step-by-step explanation:
Hey!
The way we solve this, is instead of solving for the pool and then the deck, we can solve for just the deck!
the deck adds a foot on any side of the pool, so we would add a foot to each of our dimensions!
14+1 = 15
25+1 =26
So now we add!
15+15+26+26 = 82
We need 82 feet of fencing
Hope this helps!^^
How do you graph y=3x-2
Answers
Answer:
The graph should look almost exactly like this. I used a virtual graphing chart to assist, since it is capable of showing more than paper alone.
Answer:
Here is your answer.
Step-by-step explanation:
Question 3(Multiple Choice Worth 1 points)
(05.02 MC)
Solve the system of equations using substitution.
4x + 2y = 6
x = 2y + 4
(1, 1)
(2,-1)
(8,2)
(10,3)
Answers
Answer:
(2,-1)
Step-by-step explanation:
We can use substitution to solve this system of equations. Since x is already solved for in the second equation, we can substitute 2y + 4 for x in the first equation:
4(2y + 4) + 2y = 6
Simplifying the left side:
8y + 16 + 2y = 6
Combining like terms:
10y + 16 = 6
Subtracting 16 from both sides:
10y = -10
Dividing both sides by 10:
y = -1
Now that we know y, we can use the second equation to find x:
x = 2y + 4
x = 2(-1) + 4
x = 2
Therefore, the solution to the system of equations is (x, y) = (2, -1).
The correct answer choice is (2, -1).
Consider the line 3x+2y=-1.
Find the equation of the line that is perpendicular to this line and passes through the point (5, 3).
Find the equation of the line that is parallel to this line and passes through the point (5, 3).
Note that the ALEKS graphing calculator may be helpful in checking your answer.
Equation of perpendicular line:
Equation of parallel line:
0
Answers
The given line is in the form Ax + By = C, where A = 3, B = 2, and C = -1. To find the slope of this line, we can rearrange the equation in slope-intercept form (y = mx + b), where m is the slope:
3x + 2y = -1
2y = -3x - 1
y = (-3/2)x - 1/2
The slope of the given line is -3/2. Since a line perpendicular to this line will have a negative reciprocal slope, we can find the perpendicular slope by taking the negative reciprocal of -3/2:
Perpendicular slope = -1 / (-3/2) = 2/3
Now we have the slope of the perpendicular line, and we can use the point-slope form of a line (y - y₁ = m(x - x₁)) to find its equation. Plugging in the values (5, 3) for (x₁, y₁) and 2/3 for m:
y - 3 = (2/3)(x - 5)
Expanding and simplifying:
3y - 9 = 2x - 10
2x - 3y = 1
Therefore, the equation of the line that is perpendicular to 3x + 2y = -1 and passes through the point (5, 3) is 2x - 3y = 1.
To find the equation of a line parallel to the given line and passing through the point (5, 3), we can use the same method. Since parallel lines have the same slope, the slope of the parallel line will also be -3/2.
Using the point-slope form with (5, 3) and -3/2:
y - 3 = (-3/2)(x - 5)
Expanding and simplifying:
2y - 6 = -3x + 15
3x + 2y = 21
Therefore, the equation of the line that is parallel to 3x + 2y = -1 and passes through the point (5, 3) is 3x + 2y = 21.
what is the product of 25 and (6/5n + 3 1/4)
Answers
Answer:
999
Step-by-step explanation:
Determine the value of x in the figure below:
x = 3
x = 1.7
x = 5
x = 4
Answers
Hello!
x = the intersection
5x + 3 = 2x + 15
5x - 2x = 15 - 3
3x = 12
x = 12/3
x = 4
Answer: X=4
Step-by-step explanation: 5x + 3 and 2x + 15 are congruent. sub tract 3 from each side, 5x and 2x + 12 are equal. Subtract 2x from each side, 3x and 12 are equal. Divide each side by 3 and get X=4
Can someone please feel where to put the numbers on the number line please I will give u brilliant
Answers
Answer:
-2: Start from 0 and go two steps to the left.
-4: Start from 0 and go four steps to the left.
-6: Start from 0 and go six steps to the left.
-8: Start from 0 and go eight steps to the left.
And the numbers are decreasing.
Mia hired a moving company. The company charged $500 or its services, and Mia gives the movers a 16% tip.
Answers
Answer:
The company charged $500 for its services,and Mia gives the movers a 16% tip. Now, we can add the tip amount to the cost of the service to find the total amount Mia paid: Total amount = Cost of service + Tip amount = $500 + $80 = $580
Step-by-step explanation:
5
the square root of 55
7
the square root of 32
Answers
Answer:
the square root of 55, or 7.42
Step-by-step explanation:
Use the Pythagorean Theorem, or a²+b²=c², where a and b are the sides or "legs" of the triangle and c is the hypotenuse.
a is 3, b is x, and c is 9
If you plug that into the equation, you get 3²+x²=8²
We can make this 9+x=64 by squaring the 3 and 8.
Then we can subtract 9 from each side to get x=55.
Finally, take the square root of 55 to get √55 or 7.42.
I hope this helped!
Talwar wants to invest R5800 at simple interest rate of 12,2% per annum. How many years will it take for the money to grow to R26100
Answers
It will take approximately 28.67 years for Talwar's investment of R5,800 to grow to R26,100 at a simple interest rate of 12.2% per annum.
To calculate the number of years it will take for Talwar's investment to grow to R26,100 at a simple interest rate of 12.2% per annum, we can use the formula for simple interest:
Simple Interest = Principal × Rate × Time
Given that the principal (P) is R5,800, the rate (R) is 12.2% (or 0.122 as a decimal), and the desired amount (A) is R26,100, we need to find the time (T) it will take. Rearranging the formula, we get:
Time = (Amount - Principal) / (Principal × Rate)
Plugging in the values, we have:
Time = (R26,100 - R5,800) / (R5,800 × 0.122)
= R20,300 / R708.6
≈ 28.67 years
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Kendra is researching the lowest recorded temperatures in four different cities. She wants to plot the lowest temperatures on a vertical number line. The lowest recorded temperatures of the cities are shown in the table below.
City Lowest Recorded Temperature
Morgantown 7°F below 0
Charlotte 6°F above 0
Huntsville 4°F above 0
Bluefield 8°F below 0
On a vertical number line, the point representing Morgantown's lowest recorded temperature should be plotted above the point representing
lowest recorded temperature.
On a vertical number line, the point representing Huntsville's lowest recorded temperature should be plotted below the point representing
lowest recorded temperature.
Answers
The attached number line represents points of the lowest recorded temperatures
How to represent the points on a number line?The table is given as:
City Lowest Recorded Temperature
Morgantown 7°F below 0
Charlotte 6°F above 0
Huntsville 4°F above 0
Bluefield 8°F below 0
To rewrite the table, we use the following representations:
Above 0 means positiveBelow 0 means negativeSo, we have:
City Lowest Recorded Temperature
Morgantown -7
Charlotte 6
Huntsville 4
Bluefield -8
See attachment for the number line that represents the above points
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The scatter plot shows students scores for quiz 1 and quiz 2. a. What is the quiz 1 score for a student who earned a score of 13 on quiz 2? b. Did any student(s) earn the same score on both quiz 1 and quiz 2? Explain. c. The dotted line shows the line of best fit. Write its equation and then interpret the meaning of the slope and y-intercept. Does the y-intercept make sense in the context of the problem? The slope should be represented as a fraction or whole number just to let you know. Here is a picture attached of the graph.
Answers
b) Looking at the graph, the scores of quiz 2 are on the y axis while the scores of quiz 1 are on the y axis. Each samll box on both axes is 2 units. This means that half of a samll box is 1 unit. We can locate a score of 15 in quiz 2(halfway between 14 and 16). It also corresponds to a score of 15 in quiz 1. Thus, 1 student earned 15 marks in quiz 1 and 2
c) The equation of the line of best fit is written in the slope intercept form which is expressed as
y = mx + b
where
m = slope
b = y intercept
We would calculate the slope by applying the formula,
m = (y2 - y1)/(x2 - x1)
where
y1 and y2 are y coordinates of initial and final points on the line.
x1 and x2 are x coordinates of initial and final points on the line.
Picking points on the graph, we have
when x1 = 10, y1 = 8
when x2 = 16, y2 = 14
By substituting these values into the formula,
m = (14 - 8)/(16 - 10) = 6/6 = 1
We would find the y intercept by substituting m = 1, x = 10 and y = 8 into the slope intercept equation. We have
8 = 1 * 10 + b = 10 + b
b = 8 - 10
b = - 2
Substituting m = 1 and b = - 2 into the slope intercept equation, the equation of the line of best fit is
y = x - 2
The slope is 1 and since it is small, it tells us that for each score of 1 that a student gets in quiz 2, he would likely get a score of 1 in quiz 1.
Since the y intercept is negative, it doesn't make sense in the concept of the problem because a student cannot earn a negative score in any of the quizzes. The y intercept tells us that the student earned - 2 in quiz 2 and 0 in quiz 1
EXTREMELY URGENT Which function, g or h, is the inverse function for function ƒ?
the function h because the graphs of ƒ and h are symmetrical about the line y = x
the function g because the graphs of ƒ and g are symmetrical about the line y = x
the function h because the graphs of ƒ and h are symmetrical about the x-axis
the function g because the graphs of ƒ and g are symmetrical about the x-axis
Answers
Answer:
The answer is The function g because the graphs of ƒ and g are symmetrical about the line y = x
Step-by-step explanation:
A function and its inverse function become symmetrical across the line y = x.
HELP ME PLEASE I DONT UNDERSTAND
Answers
Answer:
6.75
Step-by-step explanation:
divide 4.50 by 40 to find the cost per pencil
4.50 ÷ 40 = .1125
each pencil costs .1125 or 11.25 cents, keep the cost per pencil as .1125
then multiply .1125 by 60. because each pencil costs
.1125 and there are 60 pencils the answer is 6.75
Justin and Hayley conducted a mission to a new planet, Planet X, to study arm length. They took a random sample of 100 Planet X residents. Then they calculated a 95% confidence interval for the mean arm length.
Answers
Answer:
The correct answer is I am 95% sure that this interval includes the population mean arm length.
Note: Kindly find an attached image or copy of the complete question to this solution below:
Sources: The complete question was researched from Quizlet and Course hero sites.
Step-by-step explanation:
Solution
From the given question, i will say that I am 95 % confident interval that this interval include the population mean arm length is correct because using sample mean and confidence level we can obtain an interval which gives us the certain level of confidence that population mean is within this interval and here we are 95% confident that population mean is within this interval.
what is the y- intercept from the table
Answers
-1 because y-intercept is where y meets zero, therefore the y intercept of this graph would be -1<3