Answer:
95% confidence interval for the population is; -0.9525 < [tex]p[/tex] < -0.9505
Step-by-step explanation:
Given the data in the question;
correlation coefficient y between output and time under a load of 588 N was −0.9515
so first we determine the quantity W.
we know that; W = [tex]\frac{1}{2}[/tex]ln([tex]\frac{1 + r}{1 - r}[/tex])
we substitute -0.9515 for r
W = [tex]\frac{1}{2}[/tex]ln([tex]\frac{1 + (-0.9515 )}{1 - (-0.9515 )}[/tex])
W = [tex]\frac{1}{2}[/tex]ln([tex]\frac{1 - 0.9515 )}{1 + 0.9515 )}[/tex])
W = [tex]\frac{1}{2}[/tex]ln([tex]\frac{ 0.0485}{1.9515 }[/tex])
W = [tex]\frac{1}{2}[/tex]ln( 0.02485 )
W = [tex]\frac{1}{2}[/tex]( -3.6948975 )
W = - 1.8474
So the quantity W is normally distributed with standard deviation given by;
σ[tex]_w[/tex] = 1 / √(n - 3)
given that n is 33,000, we substitute
σ[tex]_w[/tex] = 1 / √(33,000 - 3)
σ[tex]_w[/tex] = 1 / √32997
σ[tex]_w[/tex] = 0.0055
Now, at 95% confidence interval, μ[tex]_w[/tex] will be;
⇒ - 1.8474 - 1.96( 0.0055 ) < μ[tex]_w[/tex] < - 1.8474 + 1.96( 0.0055 )
⇒ - 1.8474 - 0.01078 < μ[tex]_w[/tex] < - 1.8474 + 0.01078
⇒ -1.8582 < μ[tex]_w[/tex] < -1.8366
So to obtain 95% confidence interval for p, we use the following equation;
we transform the inequality
p = [( [tex]e^{2u_w} - 1[/tex] ) / ( [tex]e^{2u_w} + 1[/tex] )]
we substitute
[tex]\frac{e^{2(-1.8582 )}-1}{e^{2(-1.8582 )} + 1}[/tex] < [tex]\frac{e^{2u_w} - 1}{e^{2u_{w}} + 1}[/tex] < [tex]\frac{e^{2(-1.8366)}-1}{e^{2(-1.8366)} + 1}[/tex]
[tex]\frac{e^{-3.7164}-1}{e^{-3.7164} + 1}[/tex] < [tex]\frac{e^{2u_w} - 1}{e^{2u_{w}} + 1}[/tex] < [tex]\frac{e^{-3.6732}-1}{e^{-3.6732} + 1}[/tex]
[tex]\frac{0.02432-1}{0.02432 + 1}[/tex] < [tex]\frac{e^{2u_w} - 1}{e^{2u_{w}} + 1}[/tex] < [tex]\frac{0.025395-1}{0.025395 + 1}[/tex]
[tex]\frac{-0.97568}{1.02432}[/tex] < [tex]\frac{e^{2u_w} - 1}{e^{2u_{w}} + 1}[/tex] < [tex]\frac{-0.974605}{1.025395}[/tex]
-0.9525 < [tex]p[/tex] < -0.9505
Therefore, 95% confidence interval for the population is; -0.9525 < [tex]p[/tex] < -0.9505
app 19.study
Tools
Tools
Probability
Jacob performed an experiment with a weighted die, numbered 1 to 6. He rolled the die 125 times and recorded the results.
Complete the table below.
0.232
37
24
0.176
18
0.048
0.104
22
Result of Roll
Frequency
Experimental
Probability
1
2
13
3
0.144
4
29
5
0.296
6
Reset
Submit
Answer:
[tex]1 \to 22 \to 0.176[/tex]
[tex]2 \to 13 \to 0.104[/tex]
[tex]3 \to 18 \to 0.144[/tex]
[tex]4 \to 29 \to 0.232[/tex]
[tex]5 \to 37 \to 0.296[/tex]
[tex]6 \to 6 \to 0.048[/tex]
Step-by-step explanation:
Given
[tex]n = 125[/tex]
See attachment for proper table
Required
Complete the table
Experimental probability is calculated as:
[tex]Pr = \frac{Frequency}{n}[/tex]
We use the above formula when the frequency is known.
For result of roll 2, 4 and 6
The frequencies are 13, 29 and 6, respectively
So, we have:
[tex]Pr(2) = \frac{13}{125} = 0.104[/tex]
[tex]Pr(4) = \frac{29}{125} = 0.232[/tex]
[tex]Pr(6) = \frac{6}{125} = 0.048[/tex]
When the frequency is to be calculated, we use:
[tex]Pr = \frac{Frequency}{n}[/tex]
[tex]Frequency = n * Pr[/tex]
For result of roll 3 and 5
The probabilities are 0.144 and 0.296, respectively
So, we have:
[tex]Frequency(3) = 125 * 0.144 = 18[/tex]
[tex]Frequency(5) = 125 * 0.296 = 37[/tex]
For roll of 1 where the frequency and the probability are not known, we use:
[tex]Total \ Frequency = 125[/tex]
So:
Frequency(1) added to others must equal 125
This gives:
[tex]Frequency(1) + 13 + 18 + 29 + 37 + 6 = 125[/tex]
[tex]Frequency(1) + 103 = 125[/tex]
Collect like terms
[tex]Frequency(1) =- 103 + 125[/tex]
[tex]Frequency(1) =22[/tex]
The probability is then calculated as:
[tex]Pr(1) = \frac{22}{125}[/tex]
[tex]Pr(1) = 0.176[/tex]
So, the complete table is:
[tex]1 \to 22 \to 0.176[/tex]
[tex]2 \to 13 \to 0.104[/tex]
[tex]3 \to 18 \to 0.144[/tex]
[tex]4 \to 29 \to 0.232[/tex]
[tex]5 \to 37 \to 0.296[/tex]
[tex]6 \to 6 \to 0.048[/tex]
Sin 0= 8/17 determine the value of tan?
Answer:
tan theta = 8/15
Step-by-step explanation:
Sin is equal to opposite over hypotenuse. So it means that the side opposite from theta is 8, and the hypotenuse is 17.
To find the value of the adjacent side from theta, use the Pythagorean Theorem.
a^2 + b^2 = c^2
8^2 + b^2 = 17^2
64 + b^2 = 289
Subtract 64.
b^2 = 225
Take the square root.
b = 15.
So that means:
the side opposite from theta is 8,
the side adjacent from theta is 15,
the hypotenuse is 17.
Now we take tan, opposite over adjacent, and use the values from the triangle.
tan = opposite / adjacent
tan = 8/15.
What is the height of the building? need help ASAP!
Answer:
178.2 ft
Step-by-step explanation:
[tex] \sin(60) = \frac{x}{200} \\ \frac{ \sqrt{3} }{2} = \frac{x}{200} \\ x = 100 \times \sqrt{3}[/tex]
So,
[tex]h = 5 + x = 5 + 100 \times \sqrt{3} = 178.2[/tex]
find the solution for 4x+6y=16 -7x+2y=-3
Answer:
Step-by-step explanation:
==
La longitud de una varilla es de 12 pulgadas y la de otra varilla es de
87 pulgadas. Compara la longitud de la segunda varilla a la primera
y expresa el resultado como una razón.
Answer:
Hi how are you doing today Jasmine
Experimental Probability is:
O what WILL happen
what ACTUALLY happens
o what SHOULD happen
o what I THINK will happen
This is in contrast to theoretical probability where it's what we think would happen, or predict to happen.
For example, the theoretical probability of getting heads on a coin is 1/2 = 0.50 = 50%. If you flip a coin say 1000 times and get 400 heads, then the empirical or experimental probability of getting heads is 400/1000 = 0.40 = 40%. The experimental probability is what actually happens when you do the experiment. The theoretical probability is what you predict what would happen given some list of assumptions and rules about the object.
According to the law of large numbers, the experimental probability should get closer and closer to the theoretical one assuming the theoretical probability has been calculated properly (and all assumptions are correct). If we got say 475 heads instead of 400, then we might have fairly good evidence that we have a fair coin (since 475/1000 = 0.475 is fairly close to 0.500); however, if we got something like 300 heads then we might suspect that the coin is biased toward tails than it is toward heads. The more trials you do, the better a picture you can get of it.
The city of Philadelphia has an area of 141.7 square miles (mi2) and a population of 1,579,000 residents. What is the density of the city?
Answer:
11,143.3
Step-by-step explanation:
Density measures the number of people per unit area
Density = population / area
1,579,000 / 141.7 = 11,143.30
Traveling
All changes saved
8. Morgan is traveling from Dallas, Texas to San Francisco, California. She has the choice
of two airlines. She will check two bags, wants Wi-Fi access, and does not want a meal
on the plane. She does not mind a layover if it will get her a better deal. Which of the
following would be the best deal, and how much would she save?
> Lesson 82
> Lesson 83
Answer:
24
Step-by-step explanation:
i did it
If a 100 part spinner is spun and then a coin is flipped how many possible outcomes are in the sample space for the compound event
Answer:
200
Step-by-step explanation:
Answer:
200
Step-by-step explanation:
A rectangular safe can hold 7,296 cubic inches. Gold bars that are 4 inches by 8 inches by 2 inches fit to completely fill
the safe. What is the volume of each gold bar?
(A) 14in
(B) 24in
(C) 128in
(D) 64in
Answer:
I think it's 64 in
I hope it's helps you
What is the mode out of these numbers?
63, 63, 76, 67, 75, 79, 65, 95, 68, 90
Answer:
63
Step-by-step explanation:
Mode is the number that is repeated the most, in this case its 63
PLEASE HELP! I WILL GIVE BRAINLIEST!! Six less than the quotient of a number and 4 is 11. What is the number? Let n be the unknown number
Answer:
n/4-6
Step-by-step explanation:
n/4-6
This is the expression because we need to divide n by 4 and subtract 6
The number is 68
68 divided by 4= 17
17-6=11
please helppp with this questions
Answer:
Sorry for the wait.
Step-by-step explanation:
5. the two bottom angles are the same btw
[tex]2x+2x+x-15=180\\5x-15=180\\5x-15+15=180+15\\5x=195\\5x/5=195/5\\x=39[/tex]
6. straight lines are 180
[tex]3x+17+x-9=180\\4x+8=180\\4x+8-8=180-8\\4x=172\\4x/4=172/4\\x=43[/tex]
7. another 180
[tex]2x-4+3x+5+2x+11=180\\7x-10=180\\7x-10+10=180+10\\7x=190\\7x/7=190/7\\x=27.14\\[/tex]
8. 90 degree angle
[tex]x+x+4+3x-9=90\\5x-5=90\\5x-5+5=90+5\\5x=95\\5x/5=95/5\\x=19[/tex]
Hector is training for a race. During week 1, he will run 8 miles. He plans to run
27 miles in week 12.
Which equation shows how to find x, how many more miles Hector will run in
week 12 than in week 1?
A. X + 8 = 27
B. X - 8 = 27
C. -8 + x = 27
D. 8 - x = 27
Answer:
A
Step-by-step explanation:
How you find x is you do 27-8. You get 19. If you do 19+8 and think of 19 as x, you get 27. This is why A is correct
What whole number can also be written as the fraction 9/3?
Answer:
3
Step-by-step explanation:
You can put 3 in 9 three times
which property states what you do to one side you must do to the other
Answer:
Summary. The Addition Property states that: a=bis equivalent toa+c=b+cora−c=b−c Basically, whatever you do to one side of the equal sign, you have to do to the other side.
Hope this helps!!! :)
On your first draw, what is the probability of drawing a red card, without looking, from a shuffled deck containing 6 red cards, 6 blue cards, and 8 black cards?
1/2 x 288 = ???????
What is the answer?
Answer:144
Step-by-step explanation:
Use a calculator
or 1/2 x 288 = 288/2 = 144
Answer: 144
Step-by-step explanation:
I'm assuming that the "x" in this statement is a multiplication symbol.
Multiplying any number by 1/2 or 0.5 is the same thing as dividing it by 2.
Therfore the answer is 288/2 which is 144.
A bag contains 6 red marbles, 7 blue marbles, and 4 green marbles. What is the probability that a randomly selected marble is blue?
Answer: 7/17
add all the marbles to get the total
6 + 7 + 4 = 17
there are 7 blue marbles so
7/17
what is the slope of the line?
khan academy
Answer:
4/5 is the slope
Answer:
(-5,-4) or (-4, -5)
Step-by-step explanation:
I need help please. I need the the discount and selling price. Thank you
Answer:
15.12 is the discount68.88 is the sell priceStep-by-step explanation:
When you are taking off percentages from numbers, you first want to make the percent a number. This step is super simple. Just divide the 18 by 100
This gets you 0.18
Now multiply
84 * 0.18 = 15.12
So 15.12 is the discount
Then take 84 and subtract 15.12
84 - 15.12 = 68.88
So 68.88 is the sell price
plzzzzzzzzz help me on dis
Answer:
a
Step-by-step explanation:
Easy points
What is the measure of the unknown angle?
125° 143° 140° 145°
Answer:
Step-by-step explanation:
n+37=180
n=180-37=143°
Answer:
B) 143°
Step-by-step explanation:
Since n° is supplementary to 180°, then n°=180°-37°=143°.
Dustin bowled a three-game series at a bowling alley. His scores for the three games were 178, 209, and 159. What was Dustin's average score? A) 178 Eliminate B) 179 C) 180 D) 182
Answer:
182
Step-by-step explanation:
Add 178 + 209 + 159 = 546
Then divide 546 by 3 = 182
What is the measure of angle 7?
56
84
96
124
Answer:
you need more information to answer this, it's either 84 or 56 since it's in acute angle. looks closer to 84
please help ..................
Answer:
xxyy2578
Step-by-step explanation:
A sample of 125 pieces of yarn had mean breaking strength 6.1 N and standard deviation 0.7 N. A new batch of yarn was made, using new raw materials from a different vendor. In a sample of 75 pieces of yarn from the new batch, the mean breaking strength was 5.8 N and the standard deviation was 1.0 N. Find a 90% confidence interval for the difference in mean breaking strength between the two types of yarn.
Answer:
The 90% confidence interval for the difference in mean breaking strength between the two types of yarn is (0.08N, 0.52N).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction of normal variables:
When we subtract two normal variables, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
A sample of 125 pieces of yarn had mean breaking strength 6.1 N and standard deviation 0.7 N.
This means that [tex]\mu_1 = 6.1, s_1 = \frac{0.7}{\sqrt{125}} = 0.0626[/tex]
In a sample of 75 pieces of yarn from the new batch, the mean breaking strength was 5.8 N and the standard deviation was 1.0 N.
This means that [tex]\mu_2 = 5.8, s_2 = \frac{1}{\sqrt{75}} = 0.1155[/tex]
Distribution of the difference:
[tex]\mu = \mu_1 - \mu_2 = 6.1 - 5.8 = 0.3[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0626^2+0.1155^2} = 0.1314[/tex]
Confidence interval:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = zs[/tex]
[tex]M = 1.645*0.1314 = 0.22[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 0.3 - 0.22 = 0.08N
The upper end of the interval is the sample mean added to M. So it is 0.3 + 0.22 = 0.52N
The 90% confidence interval for the difference in mean breaking strength between the two types of yarn is (0.08N, 0.52N).
I need the surface area
Answer:
Step-by-step explanation:
Answer:
40.4
Step-by-step explanation:
Use the formula if you have one, (AS = 2Ab (a+b+c)h)
Then apply.
calculate the value (1+√2)^4 - (1-√2)^4 without using table
[tex](1 + \sqrt{2^{4} }) = 5[/tex]
[tex](1 - \sqrt{2^{4} } ) = - 3[/tex]5--3=8
Please help with math
Answer:
D
Step-by-step explanation:
The other graphs are functions.
Graph A is a linear function, and C is an Absolute Value Function.
Graph B also seems to be a function.
However- I can only narrow it down to B or C. I apologize if my answer is not correct.