The correct value of μ = 549 - (z * 26.5) and (549 - μ) / 26.5 = z
(a) To find the probability that a single student randomly chosen from all those taking the test scores 549 or higher, we need to calculate the z-score and then find the corresponding probability using the standard normal distribution.
The z-score formula is given by:
z = (x - μ) / σ
Where:
x = value we are interested in (549)
μ = mean of the distribution (unknown in this case)
σ = standard deviation of the distribution (26.5)
To find the z-score, we rearrange the formula:
z = (x - μ) / σ
(z * σ) + μ = x
μ = x - (z * σ)
Now we can substitute the values and calculate μ:
μ = 549 - (z * 26.5)
To find the probability, we need to calculate the z-score corresponding to the value 549. Since the distribution is normal, we can use a standard normal distribution table or a calculator to find the probability associated with that z-score.
(b) The mean and standard deviation of the sample mean score, Ł (pronounced "x-bar"), of 30 students can be calculated using the formulas:
Mean of the Sampling Distribution (Ł) = μ
Standard Deviation of the Sampling Distribution (σŁ) = σ / sqrt(n)
Where:
μ = population mean (unknown in this case)
σ = population standard deviation (26.5)
n = sample size (30)
(c) To find the z-score that corresponds to the mean score of 549, we use the same formula as in part (a):
z = (x - μ) / σ
Substituting the values:
z = (549 - μ) / 26.5
Since we are given the mean score and need to find the z-score, we rearrange the formula:
(549 - μ) / 26.5 = z
Now we can solve for z.
Please note that the solution to part (a) will provide the value of μ, which is needed to answer parts (b) and (c).
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Provide an appropriate response, Compute the standardized test statistic x 2 to test the claim o 2.38.7 it n - 12. 52-32.4, and a -0.05. O 0.492 12.961 18.490 9.209
The standardized test statistic is 12.961
To test the claim that σ = 2.38.7 with n - 12, a = -0.05 and 52-32.4,
we need to calculate the standardized test statistic.
The appropriate response is 12.961.
So, the standardized test statistic is calculated as follows:
`x = (n - 1)s² / σ²`
Where `n` is the sample size, `s` is the sample standard deviation, and `σ` is the population standard deviation.
`n = 12, s = 52 - 32.4 = 19.6, and σ = 2.38.7`
Then, `x² = (12 - 1)(19.6)² / (2.38.7)² = 12.961`
Therefore, the appropriate response is 12.961`.
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Recall the set T form part 1 of the test: T = {(z,y) € NxN: 1≤z+y≤ 4, z 21 and y ≥ 1}. Moreover, recall the joint pmf of two discrete random variables X and Y: Pxy (z,y) = P(X = 1, Y = y) = { (1+y), if (r,y) eT 0, otherwise. (a) (1 pt) Briefly explain why X and Y are dependent random variables. (b) (2 pts) Compute E[XY]. (c) (2 pts) Determine the covariance of X and Y. Hint. Use the marginal pmf you obtained from part 1 (along with symmetry between X and Y).
(a) Explanation: In order to prove that X and Y are dependent random variables, we need to show that: pX,Y(x,y)≠pX(x)pY(y) when (x,y) ∈ T which means the joint probability of X and Y is not equal to the product of the marginal probability of X and Y.
For (x,y) ∈ T, pX,Y(x,y) = P (X=1, Y=y) = 1+y
But pX(x) = P(X=1) = Σ pX,Y(1, y) = Σ (1+y)
where the summation is taken over all y for which (1, y) ∈ T. For (1,1) ∈ T,
we get pX,Y(1,1) = 2 and pX(1) = Σ pX,Y(1,y) = 2 + 3 = 5. So, pX,Y(1,1) ≠ pX(1)pY(1) which implies that X and Y are dependent random variables.
(b) E[XY] = Σ Σ xy pX,Y(x,y) where the summation is taken over all x and y for which pX,Y(x,y) > 0.
Substituting the values, we get, E[XY] = Σ Σ xy (1+y) where the summation is taken over all (x,y) ∈ T.
So, E[XY] = (1+1) (1+1) + (1+2) (1+2) + (1+3) (1+3) = 2*2 + 3*4 + 4*6 = 2 + 12 + 24 = 38.
(c) Covariance of X and Y can be determined as follows: Cov(X,Y) = E(XY) - E(X)E(Y)Now, E(X) = Σ x pX(x) and E(Y) = Σ y pY(y)
Substituting the values, we get E(X) = 5/9 and E(Y) = 20/9
Therefore, Cov(X, Y) = E(XY) - E(X)E(Y) = 38 - (5/9) (20/9) = 38 - 100/81 = 998/81.
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In a recent year, a research organization found that 300 of the 433 respondents who reported earning less than $30,000 per year said they were social networking users. At the other end of the income scale, 353 of the 546 respondents reporting earnings of $75,000 or more were social networking users. Let any difference refer to subtracting high-income values from low-income values. Complete parts a through d below. Assume that any necessary assumptions and conditions are satisfied.
a) Find the proportions of each income group who are social networking users.
The proportion of the low-income group who are social networking users is ____
The proportion of the high-income group who are social networking users is_____
(Round to four decimal places as needed.)
b) What is the difference in proportions? _____(Round to four decimal places as needed.)
c) What is the standard error of the difference? _____(Round to four decimal places as needed.)
d) Find a 99% confidence interval for the difference between these proportions. _____
The proportion of the low-income group who are social networking users is approximately 0.6928, and the proportion of the high-income group who are social networking users is approximately 0.6464.
a) To find the proportions, we divide the number of social networking users in each income group by the total number of respondents in that group. For the low-income group, the proportion is 300/433 ≈ 0.6928. For the high-income group, the proportion is 353/546 ≈ 0.6464.
b) The difference in proportions is obtained by subtracting the proportion of the high-income group from the proportion of the low-income group. The difference is approximately 0.6928 - 0.6464 = 0.0464.
c) The standard error of the difference can be calculated using the formula SE = √[(p1(1-p1)/n1) + (p2(1-p2)/n2)], where p1 and p2 are the proportions of social networking users in each group, and n1 and n2 are the sample sizes of each group. Plugging in the values, we get SE ≈ √[(0.6928(1-0.6928)/433) + (0.6464(1-0.6464)/546)] ≈ 0.0348.
d) To construct a confidence interval for the difference between the proportions, we can use the formula CI = (difference ± critical value × SE). For a 99% confidence level, the critical value can be found using a standard normal distribution table, which is approximately 2.576. Plugging in the values, we get the 99% confidence interval ≈ (0.0464 ± 2.576 × 0.0348) ≈ (0.0464 ± 0.0685).
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(1 point) how many different ways can a race with 8 runners be completed? (assume there is no tie.)
There are 40,320 different ways the race with 8 runners can be completed.
To determine the number of different ways a race with 8 runners can be completed, we can use the concept of permutations.
In a race with no tie, the order in which the runners finish matters. We want to find the number of permutations of 8 runners.
The formula to calculate permutations is given by n!, where n represents the number of items being permuted.
In this case, there are 8 runners, so the number of different ways the race can be completed is:
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320.
Each permutation represents a unique arrangement of the runners crossing the finish line. By considering the order of finish for each runner, we account for all possible outcomes in the race.
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can some one please help. 4789658953 round to the nearest 10th
mean =
mean absolute deviation =
Answer:
i believe your answer is.
4,789,658,950
Step-by-step explanation:
99 times the sum of v and 9
Answer:
Step-by-step explanation:
99(v + 9) is all you need here.
В обращении находится 250 карандашей по 8 д. ед. за единицу, 500 ручек по 12 д. ед. за единицу, 2000 тетрадей по 10 д. ед. за единицу и 412 дневников по 14 д. ед. за единицу. Найти количество денег необходимых для обращения.
Answer:
Ты русский? на этом сайте только американцы они тебе не помогут ни чем
Step-by-step explanation:
PLEASE HELP THIS IS MATHHHHH
what inequality??????
Hi, can someone please help, and possibly explain the answer please.
Answer:
[tex]x=\frac{-(-2)\±\sqrt{(-2)^2-4(3)(0)} }{2(3)}[/tex]
Step-by-step explanation:
Quadratic formula: [tex]x=\frac{-b\±\sqrt{b^2-4ac} }{2a}[/tex] when the equation is [tex]0=ax^2+bx+c[/tex]
The given equation is [tex]1=-2x+3x^2+1[/tex]. Let's first arrange this so its format looks like [tex]y=ax^2+bx+c[/tex]:
[tex]1=-2x+3x^2+1[/tex]
[tex]1=3x^2-2x+1[/tex]
Subtract 1 from both sides of the equation
[tex]1-1=3x^2-2x+1-1\\0=3x^2-2x+0[/tex]
Now, we can easily identify 3 as a, -2 as b and 0 as c. Plug these into the quadratic formula:
[tex]x=\frac{-b\±\sqrt{b^2-4ac} }{2a}\\x=\frac{-(-2)\±\sqrt{(-2)^2-4(3)(0)} }{2(3)}[/tex]
I hope this helps!
A formula of order for approximating the first derivative of a function f gives FO) - 4.50557 for h=1 f(0) - 2.09702 for h=0.5 By using Richardson's extrapolation on the above values, a better approximation of '(0) is: 0.97318 1.00177
A better approximation of f'(0) using Richardson's extrapolation is -6.91412.
To find a better approximation of f'(0) using Richardson's extrapolation, we can apply the formula:
[tex]R(1,1) = f'(h) + (f'(h) - f'(2h))/((1/2)^1 - 1)[/tex], where h is the step size.
Given the values:
f'(1) = -4.50557 (for h = 1)
f'(0.5) = -2.09702 (for h = 0.5)
Let's calculate R(1,1):
[tex]R(1,1) = f'(1) + (f'(1) - f'(0.5))/((1/2)^1 - 1)\\ = -4.50557 + (-4.50557 - (-2.09702))/(2 - 1)\\ = -4.50557 + (-2.40855)/1\\ = -4.50557 - 2.40855\\ = -6.91412.[/tex]
Therefore, a better approximation of f'(0) using Richardson's extrapolation is -6.91412.
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The answer is 3/4 What could the question be?
Answer:
how many brain cells do you have compared to the average person?
Step-by-step explanation:
f(x) = 9x-7. If f(x)= -7, find x.
Answer: the answer is 56
Step-by-step explanation: since the f(x) is -7 it would be 9 times -7 then minus 7 and get the answer.
Help me please! I will give 20 points and Brainliest!
Rhonda has an extra credit protect to make a rectangular prism whit the volume of at least 24 in*3 . if the area of her base is 6 in*3 , which inequality would represent all the possible heights, h, of her prism in order to meet her teachers requirements
A. h > 4
B. h > 8
C. h < 4
D. h < 8
What is an outcome variable in a survey project? What
is its purpose?
In a survey project, an outcome variable refers to the variable that represents the main focus or result of interest in the study.
What is an outcome variable?In a survey project, the outcome variable, otherwise known as the dependent variable, represents the main focus or result of interest.
It is the variable researchers seek to measure or predict based on the collected data. The purpose of an outcome variable is to provide insights into the specific aspect being studied, enabling researchers to understand relationships between independent variables and the outcome.
Analyzing the outcome variable allows for drawing conclusions, identifying patterns, and determining the impact of various factors. It serves as a crucial metric for evaluating success, making informed decisions, and drawing meaningful conclusions from the survey findings.
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Which of the following statements best describes the value of the expression 6x + 7 when x = 5?
Answer:
? is there a option?
Step-by-step explanation:
Answer:
37
Step-by-step explanation:
6x+7
6(5)+7
37
What is the surface area of this right rectangular prism glass slab with dimensions of 20 inches by 3 inches by 12 inches?
a.576
b.588
c.672
d.648
Answer:
C. 672
Step-by-step explanation:
Answer:
C) 672
Step-by-step explanation:
Find the lateral surface area.
Answer:
Step-by-step explanation:
NEED HELP PLEASE AND THANK YOU.
40% of my grade
What is the relationship between the angles?!!???
Im not sure how to do this can someone please help me only answer if you know
Answer:
57%
Step-by-step explanation:
FORMULA:LESS/TOTAL × 100%
=52/92 × 100%
=56.52 %
ROUND OFF TO NEAREST WHOLE NUMBER
56.52%=57%
(because the 5 after the (.) is near 1)
Use the function f=d+1 to find the value of f when d=5.
Answer:
f = 6
Step-by-step explanation:
Plug in what you know then solve:
f = d + 1
f = 5 + 1
f = 6
e. 15 = 1.5t t=? Solve please
Answer:
E Z
10
Step-by-step explanation:
15 = 1.5t
so t = 15/1.5
= 10
Answer: t = 10
1. Switch sides
- 1.5t = 15
2. Multiply both sides by 10
- 15t = 150
3. Divide both sides by 15
4. Simplify
t = 10
Please Answer This, the question is on the picture. it needs to be a fraction
will mark brainllest if its right, no links!
Answer:
x = 19.5 or 19 1/2
Step-by-step explanation:
cos 41 = 14.7/x
x = 19.5
Guided Practice
Fill in the blank.
(z−4)(2z+1)=[tex]2z^{2}[/tex]− ___ z−4
A.
7z
B.
9
C.
7
Answer: Gradpoint answer
C.
7
Step-by-step explanation: Math.way answer
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
Exact Form:
z = 0 , 7/ 4
Decimal Form:
z = 0 , 1.75
Mixed Number Form:
z = 0 , 1 3/ 4
Answer:
7
Step-by-step explanation:
(z – 4)(2z + 1) = z(2z + 1) – 4(2z + 1) = 2z2 + z – 8z – 4 = 2z2 – 7z – 4
The second term is –7z, so 7 fills in the blank.
Find the area of the shaded sector.
how many yards are in 1 foot?
correct=brainliest
Answer:
0.333333
Step-by-step explanation:
0.333 yards are in one foot
The Environmental Protection Agency (EPA) requires that cities monitor over 80 contaminants in their drinking water. Samples from the Lake Huron Water Treatment Plant gave the results shown here. All observations were below the allowable maximum, as shown by the reported range of contaminant levels. (presumably the mean would be the midrange) Allowable Substance Range Detected Maximum Origin of Substance Chromium 0.45 to 8.61 100 Discharge from steel and pulp mills, natural erosion Barium 0.006 to 0.018 2 Discharge from drilling wastes, metal refineries, natu Fluoride 1.04 to 1.14 Natural erosion, water additive, discharge from fertil aluminum factories For each substance, estimate the standard deviation o by assuming uniform distribution and normal distribution shown in Table 8.11 in Section 8.8. (Round your answers to 4 decimal places.) Uniform Distribution Normal Distribution Chromium Barium Fluoride
(i) The uniform and normal distribution for chromium is 2.4927 and 16.5762. (ii) The uniform and normal distribution for Barium is 0.0031 and 0.3323. (iii) The uniform and normal distribution for Fluoride is 0.0289 and 0.0167
For each substance, the standard deviation o is estimated by assuming uniform distribution and normal distribution. The uniform distribution standard deviation is computed using the formula as follows:
o = (b-a) / √12
where
a is the minimum value,
b is the maximum value.
The normal distribution standard deviation is calculated using the formula as follows:
o = (b - a) / 6.
Estimate the standard deviation o for each substance. Round your answers to 4 decimal places. Substance Chromium Barium Fluoride Uniform Distribution. The range of contaminant levels for chromium is from 0.45 to 8.61. The minimum value is 0.45 and the maximum value is 8.61.
(i) Chromium
Uniform distribution
o = (b-a) / √12
= (8.61 - 0.45) / √12
= 2.4927
≈ 2.4927 (rounded to 4 decimal places)
Normal Distribution
The maximum value for chromium is 100 and the minimum value is 0.45. Thus, the standard deviation o for chromium using normal distribution is:
o = (b-a) / 6
= (100 - 0.45) / 6
= 16.5762
≈ 16.5762 (rounded to 4 decimal places)
(ii) Barium
Uniform Distribution
The range of contaminant levels for barium is from 0.006 to 0.018. The minimum value is 0.006 and the maximum value is 0.018.
Thus, the standard deviation o for barium using uniform distribution is:
o = (b-a) / √12
= (0.018 - 0.006) / √12
= 0.0031
≈ 0.0031 (rounded to 4 decimal places)
Normal Distribution
The maximum value for barium is 2 and the minimum value is 0.006. Thus, the standard deviation o for barium using normal distribution is:
o = (b-a) / 6
= (2 - 0.006) / 6
= 0.3323
≈ 0.3323 (rounded to 4 decimal places)
(iii) Fluoride
Uniform Distribution
The range of contaminant levels for fluoride is from 1.04 to 1.14. The minimum value is 1.04 and the maximum value is 1.14. Thus, the standard deviation o for fluoride using uniform distribution is:
o = (b-a) / √12
= (1.14 - 1.04) / √12
= 0.0289
≈ 0.0289 (rounded to 4 decimal places)
Normal Distribution
The maximum value for fluoride is 1.14 and the minimum value is 1.04. Thus, the standard deviation o for fluoride using normal distribution is:
o = (b-a) / 6
= (1.14 - 1.04) / 6
= 0.0167
≈ 0.0167 (rounded to 4 decimal places).
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Complete Question:
The Environmental Protection Agency (EPA) requires that cities monitor over 80 contaminants in their drinking water. Samples from the Lake Huron Water Treatment Plant gave the results shown here. Only the range is reported, not the mean.
For each substance, estimate the standard deviation σ by using one of the methods shown in Table 8.11 in section 8.8. (Round your answers to 4 decimal places.)
(i) The uniform and normal distribution is Chromium.
(ii) The uniform and normal distribution is Barium.
(iii) The uniform and normal distribution is Fluoride.
Solve the inequality below and identify the correct answer: X - 2<-4
Answer:
x < -2 ?
Step-by-step explanation:
PLSSS HELP IF YOU KNOW THISS:))
Solve X
[tex] {16}^{ \frac{1}{5} } \times {2}^{x} = {8}^{ \frac{3}{4} } [/tex]
I got X= 9/10
am I right?
16^1/5 = 2^4/5 .. & .. 8^3/4 = 2^9/4
____________
2^4/5 × 2^x = 2^9/4
2^16/20 × 2^x = 2^45/20
2^[ ( 16/20 ) + x ] = 2^45/20
16/20 + x = 45/20
x = 45/20 - 16/20
x = 29/20