The sampled population is normally distributed, with the given information. (Round your answers to two decimal places.) n = 13, x 29.3, and o = 6.3 = (a) Find the 0.95 confidence interval for u. to (b) Are the assumptions satisfied? Explain. O Yes, the sampled population is normally distributed. O No, the sample distribution is not normally distributed. O not enough information
Answers
(a) The 0.95 confidence interval for μ (population mean) is (23.65, 34.95).
Using the formula for confidence intervals with the given values of sample size (n = 13), sample mean (x = 29.3), sample standard deviation (σ = 6.3), and a 0.95 confidence level, we calculate the margin of error by multiplying the critical value (2.18, obtained from the t-distribution) with the standard error (σ/√n). Adding and subtracting the margin of error from the sample mean gives us the confidence interval.
(b) We cannot determine if the assumptions are satisfied based on the given information.
The statement "The sampled population is normally distributed" is insufficient to assess the assumptions. Without additional information about the sampling method or any data indicating normality, we cannot conclusively determine if the assumptions for normal distribution are satisfied or not.
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Related Questions
A company uses two backup servers to secure its data. The probability that a server fails is 0.21.
Assuming that the failure of a server is independent of the other servers, what is the probability that one or more of the servers is operational? (Round your answer to 6 decimal places.)
Answers
0.955900 is the probability that one or more of the servers is operational.
To find the probability that one or more of the servers is operational, we can calculate the complement of the event that both servers fail, and then subtract it from 1.
Let's denote:
P(A) = probability of the first server failing = 0.21
P(B) = probability of the second server failing = 0.21
Since the failure of one server is independent of the other server, the probability of both servers failing can be calculated as the product of their individual failure probabilities:
P(A and B) = P(A) * P(B) = 0.21 * 0.21 = 0.0441
The complement of this event (at least one server is operational) is 1 - P(A and B). Therefore, the probability that one or more of the servers is operational is:
P(at least one server operational) = 1 - P(A and B) = 1 - 0.0441 = 0.9559
Rounded to 6 decimal places, the probability is approximately 0.955900.
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What is the length of the missing side? *NOTE: side lengths of 10 and 12.
Answers
Answer:
i think its 2 but i am not sure
15 first-year algebra students are learning how to solve two-step equations. the teacher notices that the students are not using precise mathematical language. which two instructional strategies should the teacher employ to encourage students to use precise mathematical language when completing this task? choose 2 answers
Answers
Solving an equation in algebra - mathematics will BOMDAS rule. Multiplication, division, addition, and subtraction are performed before.
However, in order to simplify things, if there are any exponential or logarithmic components, solve them first before applying BOMDAS to reduce them to a single solvable term. This is required by the rules.
So the list goes as
1. Exponents
2. Roots
3. Multiplication
4. Division
5. additional
6. Subtraction
However. Using a regular or scientific calculator will generate a lot of debate. A scientific calculator will adhere to the principles, while a typical calculator will evaluate from left to right or precisely the operator used first.
Using a scientific calculator, 5+2x3=11 instead of the normal one's 5+2x3=21.
Furthermore, the preferred behavior norm for division and multiplication is different.
Thus, people's difficulty with mathematics is not unjustified. The choice of how you want to approach it is ultimately up to you.
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What kinds of quadrilateral is the shape shown? The matching arrow labels indicate that two opposite sides are parallel. (Remind me about the shapes 5 5
Answers
The quadrilateral in the picture is a square since all four sides are equal.
The angles are all equal and all are right angles.
Clearly, the quadrilateral is a square.
What is the y intercept of the line described by the equation down below y=3x-6
Answers
Answer:
y-int = (0, -6)
Step-by-step explanation:
The y-intercept is the b-value of the equation of the line y = mx+b
To find the y-intercept plug in 0 for the x-value:
y=3(0) - 6
y= -6
-> x = 0, y = -6
The average number of miles (in thousands) that a car's tire will function before needing replacement is 65 and the standard deviation is 17. Suppose that 50 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution. b. What is the distribution of ¯xx¯? ¯xx¯~ N( ? ), (?) c. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 67.4 and 69.6? d. For the 50 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 67.4 and 69.6 ?
Answers
A standard normal distribution table or a calculator that can perform the calculations based on the given z-scores.
To solve these problems, we'll use the properties of the normal distribution. Let's go through each question step by step:
b. What is the distribution of ¯xx¯? ¯xx¯~ N( ? ), (?)
The average of a sample follows a normal distribution with the same mean as the population and a standard deviation equal to the population standard deviation divided by the square root of the sample size. In this case, the population mean is 65, and the population standard deviation is 17. Since we have 50 randomly selected tires, the sample size is 50.
Therefore, the distribution of the sample mean ¯xx¯ is ¯xx¯~N(65, 17/√50).
c. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 67.4 and 69.6?
To find this probability, we need to standardize the values using the z-score formula:
z = (x - μ) / σ
where x is the value we're interested in, μ is the population mean, and σ is the population standard deviation.
For 67.4:
z1 = (67.4 - 65) / 17
For 69.6:
z2 = (69.6 - 65) / 17
We can now use these z-scores to find the probabilities associated with the values using a standard normal distribution table or a calculator. The probability will be the difference between the two probabilities:
P(67.4 ≤ x ≤ 69.6) = P(z1 ≤ Z ≤ z2)
d. For the 50 tires tested, find the probability that the average miles (in thousands) before the need for replacement is between 67.4 and 69.6?
Since we're dealing with the average of the sample, we use the distribution ¯xx¯~N(65, 17/√50) as calculated in part b.
Again, we'll use the z-score formula to standardize the values:
z1 = (67.4 - 65) / (17 / √50)
z2 = (69.6 - 65) / (17 / √50)
Using these z-scores, we can find the probability:
P(67.4 ≤ ¯xx¯ ≤ 69.6) = P(z1 ≤ Z ≤ z2)
Please note that to obtain the precise probabilities, we would need to use a standard normal distribution table or a calculator that can perform the calculations based on the given z-scores.
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Write the simplified expression for the rectangle's perimeter
Answers
Answer:
P = 20x + 6
Step-by-step explanation:
\(P=2l+2w=2(6x)+2(4x+3)\)
\(P=12x+8x+6\)
\(P=20x+6\)
Hope this helps
What did this student do incorrectly to find the percent change from 14 dollars to 10 dollars?
Answers
Answer:
I don't know what he did wrong, but to work out the percentage change, you do 10 ÷ 14, which gives you 0.71.
1 - 0.71 = 0.29
0.29 × 100 = 29% You multiply by 100 to get your percentage change value.
29% is the percentage change.
I hope this helps you!! ^-^
19. Graph the function 3x + 2y = 8 with the given
domain: (-2,0, 2, 4}
TEK 3C
Justify/Show your work:
Answers
Answer:
Step-by-step explanation:
How to Write 9 in Roman Numerals?
Answers
To write 9 in Roman Numerals, you would use the symbols "IX".
The symbol "I" represents the number 1 and the symbol "X" represents the number 10. When a smaller symbol is placed before a larger symbol, it means that the smaller symbol is subtracted from the larger symbol.
In this case, "I" is placed before "X", so it is subtracted from 10, giving us the value of 9.
Here is a step-by-step explanation:
1. Identify the symbols for 1 and 10: "I" and "X"
2. Place the smaller symbol before the larger symbol: "IX"
3. Subtract the smaller symbol from the larger symbol: 10 - 1 = 9
4. The result is the value of the Roman Numeral: "IX" = 9
Therefore, the Roman Numeral for 9 is "IX".
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Draw the graph of y= -6
Answers
Answer:
See attachment.
Step-by-step explanation:
How does affordance contribute to motor development?
Answers
1. Affordably presented by objects or environments, such as a ball providing the opportunity to practice grasping, throwing, and catching.
2. Individuals perceive these affordances and decide to engage with them, based on their current motor abilities and developmental stage.
3. Through interacting with affordances, individuals practice and develop their motor skills by attempting, refining, and mastering the actions associated with affordance.
Affordably is a term used to describe the relationship between an individual's perception of their environment and their ability to interact with it. In terms of motor development, affordances refer to the opportunities for movement that the environment presents. These opportunities can be both physical and social and can include objects to manipulate, spaces to explore, and people to interact with.
The concept of affordance is important for motor development because it provides children with opportunities to practice and refine their motor skills. As children explore their environment, they are able to perceive the various affordances that it presents, and they can use these affordances to develop their motor skills.
For example, a child may perceive that a box can be used as a stepping stool, and they may use this affordance to climb up onto a table. In doing so, they are developing their balance, coordination, and strength. Similarly, a child may perceive that a ball can be thrown, caught, and bounced, and they can use these affordances to develop their hand-eye coordination, spatial awareness, and timing.
Overall, affordance plays an important role in motor development by providing children with opportunities to explore and interact with their environment and to develop their motor skills in the process.
Affordance contributes to motor development by providing opportunities for individuals to interact with their environment, which in turn helps them develop and refine their motor skills. Affordance refers to the potential actions or uses that an object or environment provides to an individual. In the context of motor development, affordances can be seen as opportunities for practicing and enhancing motor abilities.
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On Monday at the county fair , Jared played a game and won 75 tickets . On Tuesday , he won 105 tickets on Wednesday , he won 127 tickets , but the spent 250 of them on a prize . How many more tickets does Jared need to win a prize that costs 150 tickets ?
Answers
Answer: 93
Step-by-step explanation:
75+105+127= 307
307-250= 57
150-57= 93 (57 + 93 = 150)
What is the quotient property of exponents?
Answers
Answer:
when you divide powers with the same base, you can just subtract the exponents
states that when dividing two powers with the same base, we would subtract exponents
a^m • a^n = a^m+n
(a^m)^n=a^m^n
A function that models the profit for a new pet-monitoring system shows that there is no profit made until the price reaches $95 per unit, a maximum profit at a price of $140 per unit, and no profit at a price over $185 per unit. Which graph models the function?
Answers
The profits at x = $185 is 0 and the graph is attached below:
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Function is to model the profits of a new pet-monitoring system, so, if the profits are y and x then y = f(x)
The curve shows that y is negative at values of x< $95, then the profits increase when x varies between $95 and $140.
The profits reach a maximum at $140 and then the profits start to reduce as x increases again.
So, the profits at x = $185 is 0.
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Answer:
a on edge
Step-by-step explanation:
I js did it
What are the endpoint coordinate for the midegment of △PQR that i parallel to PR¯¯¯¯¯?
Answers
point coordinates for the mid segment of the parallel to PQ segment of the PQR is ST point is (-3.5, 0.5) and (-1, -0.5).
Given that,
We have to find what are the endpoint coordinates for the middle portion of the parallel to PQ segment of the PQR.
We know that,
First we write the co-ordinates of the triangle in the given graph.
P is (-3,3)
Q is (2,1)
R is (-4,-2)
The triangle's midpoint, which is parallel to section PQ, must be located. As a result, we would need to locate the midpoints of the segments PR and QR before joining the points to obtain the mid segment.
Midpoint Formula is
(x₁+x₂/2, y₁+y₂/2)
So,
The midpoint of the side PR is
(-3+(-4)/2, 3+(-2)/2)
(-3-4/2, 3-2/2)
(-7/2,1/2)
So, S point is (-3.5, 0.5)
The midpoint of the side QR is
(2+(-4)/2, 1+(-2)/2)
(2-4/2, 1-2/2)
(-2/2,-1/2)
So, T point is (-1, -0.5)
Therefore, The endpoint coordinates for the mid segment of the parallel to PQ segment of the PQR is ST point is (-3.5, 0.5) and (-1, -0.5).
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Please share how you believe your experiences, perspectives, and/or skills have shaped your ability to contribute to a diverse learning environment.
Answers
My experiences, perspectives, and skills have all played a significant role in shaping my ability to contribute to a diverse learning environment. As someone who has traveled extensively and lived in various parts of the world, I have been exposed to different cultures and ways of thinking.
In addition, my work in various fields has given me a range of skills that are useful in a diverse learning environment. For example, my experience in teaching, writing, and public speaking has helped me to communicate effectively with people from different backgrounds and to tailor my approach to meet their needs.
Overall, I believe that my experiences, perspectives, and skills have equipped me to contribute to a diverse learning environment in a positive and meaningful way. Whether I am working with students or colleagues, I strive to be respectful, empathetic, and open-minded, and to create a welcoming and inclusive space for everyone.
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2x + y + 6z = + 1
3x + 2y + 5z = 16
7x + 3y - 4z = 11
Answers
Answer:
1) x=1/2-y/2-3z
2)x= 16/3- 2y/3- 5z/3
3)x= 11/7- 3y/7+ 4z/7
Step-by-step explanation:
isolate the variable, to do that divide each side by the factors that don't contain the variable
Express 3.23×10 ^6
in standard decimal notation.
Answers
The number 3.23×10^6, expressed in standard decimal notation, is 3,230,000. In scientific notation, a number is expressed as the product of a coefficient and a power of 10.
In this case, the coefficient is 3.23, and the power of 10 is 6. To convert this number into standard decimal notation, we need to multiply the coefficient by the corresponding power of 10. The power of 10, in this case, is 10^6, which means 10 raised to the power of 6. This is equivalent to 1 followed by six zeros: 1,000,000. To obtain the standard decimal notation, we multiply the coefficient, 3.23, by 1,000,000.
Calculating the multiplication, we have:
3.23 × 1,000,000 = 3,230,000.
Hence, the number 3.23×10^6, expressed in standard decimal notation, is 3,230,000. This means that the number is equal to 3.23 million.
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what expression is equivalent to -5(x)+(-4)(-3)
Answers
Answer:-25+-12
Step-by-step explanation:so I made x value as 5 so I multiplied -5x5 and it's -25 then I multiplied -4x-7 and that's -12 so the equivalent expression for my way is -25+-12
helpppp pls
Members at the Star Theater pay $30.00 per month plus $1.95 for each movie. Nonmembers pay the regular $7.95 admission fee. How many movies would both a member and a nonmember have to see in a month to pay the same amount?
Answers
Explanation;
Members have to pay $30 a month just to have a lower admission fee. So members already start with a high price. If you add 7.95 together 5 times you get 39.75. This is the same as the members when you add the $30 admission fee to the 5 movies. (30+1.95....). That is how you find that both members and nonmembers will be paying the same amount after both watching 5 movies.
The weight of four puppies are shown in pounds 9.5 9 3/8 9.125 9 3/4 which list shows these weights in order from greatest to least?
Answers
Answer:
9. 3 ÷ 4, 9.5, 9. 3 ÷ 8, 9.125
Step-by-step explanation:
Given that
The weight of four puppies are 9.5 9 3 ÷ 8 9.125 9 3 ÷ 4
We need to find out the weight from high to low
So,
First we place the number in decimals
After this, we line all up
Now place the numbers from high to low
The above shows the correct order
Therefore the same would be considered and relevant
HELP!!! use the law of sines!
Answers
Answer:
21.28
Step-by-step explanation:
Hey There!
So the law of sines says
\(\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}\)
To solve for c we just plug in the values that are given to us
\(\frac{25}{sin38} =\frac{c}{sin31.6}\)
step 1 multiply each side by sin31.6
now we have
\(c=\frac{25sin31.6}{sin38} \\c=21.2773548\)
assuming that you have to round
if you're supposed to round to the nearest whole number then the answer is 21
if you're supposed to round to the nearest tenth then the answer is 21.3
if you're supposed to round to the nearest hundredth then the answer is 21.28
Which ordered pair is a solution to the system of inequalities graphed here?
Answers
Answer:
c
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
If you plot the point (1, 4), you see that the ordered pair falls in the shaded area bounded by the lines. The other ordered pairs fall outside of the shaded area.
Add.
(56² − 3b + 2) + (26 — 4)
What is the answer? Enter your answer in the blanks.
Answers
Answer:
The correct answer is 5b²-b-2
Multiplication is doing what to the same number continuously?
Answers
Answer:
mutiplying it
Step-by-step explanation:
it is multiplying it because 2×2=4
Answer:
multiplying the answer
Find x, y, and z. Please Show work how you did!
Answers
Answer:
y=36,x=108,z=30
Step-by-step explanation:
1)180°=72°+(3y)°
=>(3y)°=180°-72°
=>(3y)°=108°
=>3y=108
=>y=36
2)(x)°=(3y)°=>x=108
3)(3z+18)°=108°=>3z+18=108=>3z=90=>z=30
Answer:
x = 108
y = 36
z = 30
Step-by-step explanation:
(x)° + 72° = 180° (interior angles on the same side of transversal)
-> (x)° = 180 - 72°
-> (x)° = 108°
-> x = 108
(3y)° = (x)° (corresponding angles)
-> 3y = x
-> 3y = 108
-> y = 108/3
-> y = 36
(3z + 18)° = (x)° (corresponding angles)
-> 3z + 18 = x
-> 3z + 18 = 108 - 18
-> 3z = 108 - 18
-> 3z = 90
-> z = 90/3
-> z = 30
I am a solution. If you square my number, the answer will equal 441. What number am I? (hint: there are two of me)
Answers
Answer:
(21)(21)
Step-by-step explanation:
21x21=441
21²
What is the area of the triangle at the top?
Answers
Answer:
60 degrees
Step-by-step explanation:
It is an equilateral triangle in which each angle is equal to 60 degrees
Which describes the correlation shown in the scatterplot
Answers
Hope this helps!!