Answer:
a) [tex] z= \frac{34-34}{2.5}= 0[/tex]
[tex] z= \frac{39-34}{2.5}= 2[/tex]
And we want the probability from 0 to two deviations above the mean and we got 95/2 = 47.5 %
b) [tex] P(X<31.5) [/tex]
[tex] z= \frac{31.5-34}{2.5}= -1[/tex]
So one deviation below the mean we have: (100-68)/2 = 16%
c) [tex] z= \frac{29-34}{2.5}= -2[/tex]
[tex] z= \frac{36.5-34}{2.5}= 1[/tex]
For this case below 2 deviation from the mean we have 2.5% and above 1 deviation from the mean we got 16% and then the percentage between -2 and 1 deviation above the mean we got: (100-16-2.5)% = 81.5%
Step-by-step explanation:
For this case we have a random variable with the following parameters:
[tex] X \sim N(\mu = 34, \sigma=2.5)[/tex]
From the empirical rule we know that within one deviation from the mean we have 68% of the values, within two deviations we have 95% and within 3 deviations we have 99.7% of the data.
We want to find the following probability:
[tex] P(34 < X<39)[/tex]
We can find the number of deviation from the mean with the z score formula:
[tex] z= \frac{X -\mu}{\sigma}[/tex]
And replacing we got
[tex] z= \frac{34-34}{2.5}= 0[/tex]
[tex] z= \frac{39-34}{2.5}= 2[/tex]
And we want the probability from 0 to two deviations above the mean and we got 95/2 = 47.5 %
For the second case:
[tex] P(X<31.5) [/tex]
[tex] z= \frac{31.5-34}{2.5}= -1[/tex]
So one deviation below the mean we have: (100-68)/2 = 16%
For the third case:
[tex] P(29 < X<36.5)[/tex]
And replacing we got:
[tex] z= \frac{29-34}{2.5}= -2[/tex]
[tex] z= \frac{36.5-34}{2.5}= 1[/tex]
For this case below 2 deviation from the mean we have 2.5% and above 1 deviation from the mean we got 16% and then the percentage between -2 and 1 deviation above the mean we got: (100-16-2.5)% = 81.5%
A sample of 200 observations from the first population indicated that X1 is 170. A sam- ple of 150 observations from the second population revealed X2 to be 110. Use the .05 significance level to test the hypothesis. a. State the decision rule. b. Compute the pooled proportion. c. Compute the value of the test statistic. d. What is your decision regarding the null hypothesis?
Answer:
a. If the P-value is smaller than the significance level, the null hypothesis is rejected.
b. Pooled proportion = 0.8
c. z = 2.7
d. As the P-value (0.0072) is smaller than the significance level (0.05), the null hypothesis is rejected.
There is enough evidence to support the claim that the proportions differ significantly.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
We will use the P-value approach, so the decision rule is that if the P-value is lower than the significance level, the null hypothesis is rejected.
The claim is that the proportions differ significantly.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]
The significance level is 0.05.
The sample 1, of size n1=200 has a proportion of p1=0.85.
[tex]p_1=X_1/n_1=170/200=0.85[/tex]
The sample 2, of size n2=150 has a proportion of p2=0.7333.
[tex]p_2=X_2/n_2=110/150=0.7333[/tex]
The difference between proportions is (p1-p2)=0.1167.
[tex]p_d=p_1-p_2=0.85-0.7333=0.1167[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{170+110}{200+150}=\dfrac{280}{350}=0.8[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.8*0.2}{200}+\dfrac{0.8*0.2}{150}}\\\\\\s_{p1-p2}=\sqrt{0.0008+0.00107}=\sqrt{0.00187}=0.0432[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.1167-0}{0.0432}=\dfrac{0.1167}{0.0432}=2.7[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]P-value=2\cdot P(z>2.7)=0.0072[/tex]
As the P-value (0.0072) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the proportions differ significantly.
To study the effects of an advertising campaign at a supply chain, several stores are randomly selected with the following observed before‐ and after‐advertising monthly sales revenues: Store number 1 2 3 4 5 Old sales revenue (mil. $) 6.5 4.8 7.9 6.2 7.1 New sales revenue (mil. $) 7.5 6.3 7.1 7.8 8.9 Let μ₁ and μ₂ be the means of old and new sales revenues, both in millions of dollars per month. (a)[7] At α = 0.05, test H₀: μ₂ ≤ μ₁ versus H₁: μ₂ > μ₁. Sketch the test. Interpret your result. (b)[3] Sketch and find the p‐value of the test. Would you reject H₀ if α = 0.01? Hint: Use 5 decimals. Refer to some Excel lookups: αv 0.990 0.990 0.950 0.950
Answer:
Check the explanation
Step-by-step explanation:
Part a
H0: µ2≤µ1 versus H1: µ2>µ1
(Upper tailed test)
WE will consider differences as (New – Old).
From given data, we have
Dbar = 0.70
SD = 0.70
n = 5
Degrees of freedom = df = n – 1 = 5 – 1 = 4
Test statistic = t = (Dbar - µd) /[SD/sqrt(n)]
t = (0.70 – 0)/[0.70/sqrt(5)]
t = 0.70/ 0.3130
t = 2.2361
Critical value = 2.1318
(by using t-table)
P-value = 0.0445
(by using t-table)
P-value < α = 0.05
So, we reject the null hypothesis
There is sufficient evidence to conclude that the average monthly sales revenue increases after the advertising.
Kindly check the first attached image for the graphical table.
Part b
P-value = 0.0445
α = 0.01
P-value > α = 0.01
So, we do not reject the null hypothesis
There is insufficient evidence to conclude that the average monthly sales revenue increases after the advertising.
Kindly check the second attached image for the graphical table.
Automobile racing, high-performance driving schools, and driver education programs run by automobile clubs continue to grow in popularity. All these activities require the participant to wear a helmet that is certified by the Snell Memorial Foundation, a not-for-profit organization dedicated to research, education, testing, and development of helmet safety standards. Snell "SA" (Sports Application)-rated professional helmets are designed for auto racing and provide extreme impact resistance and high fire protection. One of the key factors in selecting a helmet is weight, since lower weight helmets tend to place less stress on the neck. The following data show the weight and price for 18 SA helmets.
W p
64 252
64 283
64 190
64 197
58 291
47 702
49 907
59 341
66 202
58 305
58 477
52 477
63 379
62 377
54 563
63 255
63 286
a. Develop a scatter diagram with weight as the independent variable.
b. Does there appear to be any relationship between these two variables?
There appears to be a - Select your answer -negativepositiveItem 2 linear relationship between the two variables. The heavier helmets tend to be less expensive.
c. Develop the estimated regression equation that could be used to predict the price given the weight.
The regression equation is (to 1 decimal and enter negative values as negative numbers). If your answer is zero enter "0".
Answer:
Step-by-step explanation:
Hello!
Given the variables
X₁: Weight of a safety helmet for racers
X₂: Price of a safety helmet for racers
Note, there is n= 17 observed values for each variable so for all calculations I'll use this number and disregard the 18 mentioned in the text.
a) Scatterplot in attachment.
b) If you look at the diagram it seems that there is a negative linear regression between the price and the weight of the helmets, meaning, the higher the helmet weights, the less it costs.
c) The estimated regression equation is ^Yi= a + bXi
n= 17; ∑Y= 6466; ∑Y²= 3063392; ∑X= 1008; ∑X²= 60294; ∑XY= 367536
Y[bar]= 380.35; X[bar]= 59.29
[tex]b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} } = \frac{367536-\frac{1008*6466}{17} }{60294-\frac{(1008)^2}{17} } = -30.18[/tex]
[tex]a= Y[bar]- bX[bar]= 380.35-(-30.18)*59.29= 2169.77[/tex]
The estimated regression equation for the price of the helmets as a function of their weight is:
^Yi= 2169.77 -30.18Xi
I hope it helps!
-3183.96 cm3
-715.92 cm3
-489.84 cm3
-1469.52 cm3
Answer:
1469.52 cm3
Step-by-step explanation:
Area of a circle times the height of the cylinder.
Area of a circle = 3.14*6^2 = 113.04
113.04*13 = 1469.52 cm3
Solving One Step Equations:
z - 2.3 = 0.46
Answer:
z =2.76
Step-by-step explanation:
z - 2.3 = 0.46
Add 2.3 to each side
z - 2.3+2.3 = 0.46+2.3
z =2.76
....................
Answer:
I would love to help you but all I see is dots
Data were collected over a 10-year timespan from a sample of penguins that were randomly given either metal or electronic tags. One variable examined is the length of foraging trips. Longer foraging trips can jeopardize both breeding success and survival of chicks waiting for food. Mean length of 344 foraging trips was 12.70 days for metal-tagged penguins. Mean length of 512 foraging trips was 11.60 days for electronic-tagged penguins. An estimate of the standard error for this difference of means is SE=0.283
Question:
Data were collected over a 10-year timespan from a sample of 100 penguins that were randomly given either metal or electronic tags. One variable examined is the length of foraging trips. Longer foraging trips can jeopardize both breeding success and survival of chicks waiting for food. Mean length of 344 foraging trips was 12.70 days for metal-tagged penguins. Mean length of 512 foraging trips was 11.60 days for electronic-tagged penguins. An estimate of the standard error for this difference of means is SE=0.283.
a) We will address the question of whether foraging trips are longer on average among metal-tagged penguins than among electronic-tagged penguins. State hypotheses in terms of two means.
b. Calculate the sample statistic xM - xE
c. Calculate a t-test statistic, using the given estimate of SE.
d. What are the correct (conservative) degrees of freedom for a t-distribution for this test?
e. Use t-distribution methods to find the p-value and draw a rough curve with appropriate shaded region. You may give either a precise p-value from software or bounds on a p-value from Table A.
f. State the conclusion of the test in context, using nontechnical language.
Answer:
See explanation below
Step-by-step explanation:
a) The null and alternative hypotheses are:
H0 : uM - uE = 0
H1 : uM - uE > 0
b) Calculating the sample statistic,
xM-xE, we have:
Given xM = 12.70 days
xE = 11.60 days
xM - xE = 12.70 - 11.60 = 1.10 days
Therefore sample statistic = 1.10
c) Calculating the test statistic, using the given estimate of SE, we have:
Given standard error, SE = 0.283
[tex] \frac{xM - xE}{SE} = \frac{12.70 - 11.60}{0.283} = 3.89 [/tex]
Therefore, t test = 3.89
d) The correct degrees of freedom.
We have:
[tex]Min(n_M-1, n_E-1 ) = Min(344-1, 512-1) = Min(343, 511)[/tex]
df = 343
e) p-value:
Pvalue = P(Z > 3.89) = 0.00000602
Since p value is less than significance level of 0.05, we reject null hypothesis H0.
f) Conclusion:
There is enough evidence to conclude that foraging trips are longer on average among metal-tagged penguins than among electronic-tagged penguins.
Prove that the diagonals of a rectangle bisect each other.
The midpoints are the same point, so the diagonals _____
are parallel to each other.
bisect each other.
have the same slope.
are perpendicular to each other.
Answer:
bisect each other.
Step-by-step explanation:
The midpoints are the same point, so the diagonals bisect each other.
__
More elaboration on a proof
The alternate interior angles formed by diagonals and the sides of the triangle are congruent, so the (point-to-point) triangles formed by the crossing diagonals are congruent ASA. Since the sides of those triangles are congruent, the diagonals meet at their midpoints. That is, the diagonals bisect each other.
the radius of 2 spheres are 4 and 12. find the scale factor of the surface areas
Answer:
~ Surface Area 1 = 9 * Surface Area 2 ~
Step-by-step explanation:
Let us look through this problem step by step;
1. The formula to determine the surface area of a sphere is 4πr^2
2. Here we can see that the difference between the two radii of the spheres is that one is 3 times greater than the other
3. So if you were to think about it, in this surface area formula if the radii is squared, the difference between the two surface areas would also be squared. That means that the difference between the surface areas is 3^2, or 9 times the other.
4. This would mean the scale factor to be that one of the spheres surface area is 9 times the other ( Surface Area 1 = 9 * Surface Area 2)
Fifteen mothers were asked how many months old their babies were when they cut their first tooth. The results are shown below.
8, 8, 6, 8, 9, 10, 5, 7, 9, 5, 9, 7, 6, 8, 7
Find the range and the outlier(s), if any, of the data set.
Answer:
The range is 5, there are no outliers.
Step-by-step explanation:
To find the range, just subtract the smallest number from the largest number. In this case, the largest number is 10 and smallest number is 5. 10 - 5 is 5 so there's your answer!
What is an equation of the line that passes through the point (- 5, - 6) and is parallel to the line 4x - 5y = 35
Answer:
4x - 5y = 10
Step-by-step explanation:
Any line parallel to 4x - 5y = 35 will have the same equation EXCEPT that the constant will be different.
Starting with 4x - 5y = 35, replace x with the given x-coordinate -5 and the given y-coordinate -6, and finally the given 35 with the constant C:
4(-5) - 5(-6) = C, or
-20 + 30 = C. Thus, C = 10, and the equation of the new line is
4x - 5y = 10
The equation of line is 4x - 5y = 10
What is equation of line?A straight line's general equation is y = mx + c, where m is the gradient. On the y-axis, this number c is referred to as the intercept. Key Point y = mx + c is the equation for a straight line with a gradient of m and an intercept of c on the y-axis.
Given the points (-5,-6)
and parallel to line 4x - 5y = 35...…..(1)
the equation of line is (y - y₁) = m( x - x₁)
for parallel line condition the value of m is equal to both equations
converting eq. 1 in the form of y = mx + c
4x - 5y = 35
we get y = 4/5x -7
here m = 4/5 and c = -7
substitute the value of m in equation of line
where y₁ = -6; x₁ = -5
(y - (-6)) = 4/5(x - (-5))
y +6 = 4/5(x+5)
simplify above eq. we get
4x - 5y = 20
Hence the equation of the line that passes through the point (- 5, - 6) is 4x - 5y = 20
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What the error? Jonah says a common denominator for 3/4 and 2/5 is 9 what is Jonah error?explain
Answer:
should be 20
Step-by-step explanation:
yes
Answer: She had added the Denominator, instead of finding the LCM.
Explanation: She should've multiplied them by a common number to equal a common Product, and replace the Denominator with the Product. (The correct denominator is 20, because 4 x 5 = 20, and 5 x 4= 20)
Calculate the lateral area of the rectangular prism if the perimeter of the base is 48 units
Answer: It’s C just did assignment 288unitssquared
You have a bag of marbles that has 3 blue marbles and 4 red ones. What is the chance that you pick a blue OR a red marble?
Answer:
7/7
Step-by-step explanation:
Add up the amount of the marbles in total and read what color the marble they ask for the chances of. The color of marble should go first then the total of the marbles. (they could ask for more than one color so just add up both the colors given.)
The perimeter of a rectangle is 42feet. The length decreased by 3times the width is 1foot . What are the dimensions of the rectangle? (what is the length and width)
Answer: Length is 16 ft. Width is 5 feet.
Step-by-step explanation: Take the information given and write an equation. "Length decreased by 3 is 1" becomes L - 3w = 1 .
"Solve" for L. L= 3w +1
Write another equation for the formula of a perimeter. P=2L + 2w.
Substitute the values for L (from the first "solution" you wrote) and P (42 ft, given).
42 = 2(3w +1) + 2w. Solve this.
42= 6w +2 + 2w
42= 8w +2. Subtract 2 from both sides then divide both sides by 8.
W = 5
Substitute that into the first equation you wrote to get the Length.
L - 3(5) = 1
L -15 = 1. L = 1+15
L = 16
You buy $2,500of saving bonds at 1.7%interest.how many years will it take for your investment to equal $3000?
Answer:
It will take 12 years using simple interest
Step-by-step explanation:
2,500 x 1.7% = 42.5
42.5 x 12 + 510
2500 +510 +3010
ten tiles numbered 1 through 10 are placed in a bag you randomly chose one tile. without replacing the tile you randomly chose a second tile. Find the probability of choosing a 4 and then an even number?
Answer:
1/10
Step-by-step explanation:
there are 10 tiles and only 1 tile numbered 4 so 1 out of 10 tiles are numbered 4
Need help with Math question
Answer:
B; {x|x<-8}
Step-by-step explanation:
What is the surface area of the triangular prism?
Triangular prism
a
152 square feet
b
172 square feet
c
252 square feet
d
264 square feet
Answer:
Option c. 252 square feet
Step-by-step explanation:
This question does not have figure, please find the figure attached below.
Area of the triangular sides = [tex]2(\frac{1}{2}\times bh)[/tex]
= [tex]2(\frac{1}{2}\times 3\times 4)[/tex]
= 2(6)
= 12 feet²
Area of the rectangular base = A = b × h
= 20 × 3
= 60 feet²
Area of the lateral side = 20 × 5
= 100 feet²
Area of the vertical rectangular side = 20 × 4
= 80 feet²
Total surface area = 12 + 60 + 100 + 80
= 252 feet²
Total surface area of the triangular prism is 252 square feet.
the table shows jills math quiz scores. what is the minimum score she needs on her next quiz to have a mean of at least 92
week 1: 92
week 2: 96
week 3: 94
week 4: 88
Answer:90
Step-by-step explanation:
The minimum score she needs on her next quiz is 90
What is mean ?The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
The mean value of the data set is the ratio of sum of data set's values to number of values it has.
If the data set consists of values
Mean = Sum of observations/the number of observations
[tex]\overline{x} = \dfrac{x_1 + x_2 + \cdots + x_n}{n}[/tex]
Given;
Mean of 5 weeks= 92
Mean= (week 1 + week 2 + week 3 + week 4+ week 5)/number of weeks
let, the score of next week be x
Mean = (92+96+94+88+x)/5
putting the value of mean;
92= (370+x)/5
460=370+x
x=460-370
x=90
In the next quiz jills need 90 score to get the mean of 92.
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Consider the initial value problem y' − 9 2 y = 9t + 2et, y(0) = y0. Find the value of y0 that separates solutions that grow positively as t → [infinity] from those that grow negatively. (A computer algebra system is recommended. Round your answer to three decimal places.) y0 = How does the solution that corresponds to this critical value of y0 behave as t → [infinity]?
1, The corresponding solution converges to the function y = 9t.
2. The corresponding solution will decrease without bound.
3. The corresponding solution converges to the function y = −9t.
4. The corresponding solution converges to the function y = 0. The corresponding solution will increase without bound.
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
Factor the expression 4x + 32. Explain each step you
take in the process.
Answer:
4(x+8)
Step-by-step explanation:
4x + 32
Factorization:
4x: 2×2×x
32: 2×2×2×2×2
Highest common factor: 2×2 = 4
4x + 32
(4×x) + (4×8)
Using distributive property:
4(x + 8)
Answer:
The GCF of 4x and 32 is 4, so the first step is to divide each term by 4. The quotients are x and 8. The factored expression will be 4(x + 8).
The perimeter of a square is 32cm? What is the length of each side?
the answer is 8 because there is 4 sides on a square and 8 x 4 is 32.
What is the area of the kite? 20 36 40 80
Answer:
44
Step-by-step explanation:
20+36+40+80= 176
176/4= 44
A bag contains 10 red marbles and 5 blue marbles. What is the probability of choosing 2 red marbles without replacing the first?
Answer:
i think 5 percent but dont trust me xDDD
Step-by-step explanation:
*ill give you BRAINLIST * (have to get it right ) Write the equation of the line with the given slope and y-intercept.
slope = 1
y-intercept = - 3/7
Answer:
Y=x-3/4
Step-by-step explanation:
slope intercept form
(slope=x)(1x=x)
What is the meaning of life
Answer:
The answer of life is 42 just look it up
apply the distributive property to factor out the gcf of 35+14
Answer:
7(5 +2)
Step-by-step explanation:
From our knowledge of times tables, we know that ...
35 = 5·7
14 = 2·7
so the greatest common factor of 35 and 14 is 7. Factoring that out, we have ...
35 +14 = 7(5 +2)
Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below. Reyna got a score of 75.3; this version has a mean of 69.3 and a standard deviation of 12. Kaitlyn got a score of 228.4; this version has a mean of 206 and a standard deviation of 28. Cade got a score of 7.88; this version has a mean of 7.2 and a standard deviation of 0.4. If the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of the applicants should be offered the job?
Answer:
Due to the higher z-score, Cade should be offered the job.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
If the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of the applicants should be offered the job?
Whoever had the higher z-score.
Reyna:
Reyna got a score of 75.3; this version has a mean of 69.3 and a standard deviation of 12.
This means that [tex]X = 75.3, \mu = 69.3, \sigma = 12[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{75.3 - 69.3}{12}[/tex]
[tex]Z = 0.5[/tex]
Kaitlyn:
Kaitlyn got a score of 228.4; this version has a mean of 206 and a standard deviation of 28.
This means that [tex]X = 228.4, \mu = 206, \sigma = 28[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{228.4 - 206}{28}[/tex]
[tex]Z = 0.8[/tex]
Cade:
Cade got a score of 7.88; this version has a mean of 7.2 and a standard deviation of 0.4. This means that [tex]X = 7.88, \mu = 7.2, \sigma = 0.4[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{7.88 - 7.2}{0.4}[/tex]
[tex]Z = 1.7[/tex]
Due to the higher z-score, Cade should be offered the job.
Please what is the length of AC? Please 1 day no answer.
Answer: AC = 2.33
Step-by-step explanation:
use tangent to find the missing side
Tangent = opposite/adjacent
tan B = ?/5
tan 25 = ?/5
multiply each side by 5
? = 2.33153829.....
so
AC = 2.33
