The proportion of adults with scores above 110 is 0.1841.
Here, we have,
It should be noted that from the information illustrated, Wechsler Adult Intelligence Scale scores are approximately Normal, with a mean of 100 and a standard deviation of 11.
The formula to use will be:
P(a < Z < b) = P(Z < b) – P(Z < a)
a = lower value
b = higher value
Z = z value
It should be noted that the proportion of adults with scores above 110 will be:
= P(x > 110)
= P(z > 110 - 100/11)
= P(z > 0.90)
= 1 - 0.8159
= 0.1841
Therefore, this illustrates those that has scores of more than 110.
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How do you find the greatest common denominator, when comparing two numbers? Explain your thought process, in the example I provided. What is the greatest common Denominator for the numbers 20 and 40. Explain each step you do. Your answer will start with these words. "How to find the the greatest common denominator between 20 and 40?
Answer:
20 is the greatest common denominator. You can find this by listing the factors of each number. The highest number that can fit into both individual numbers is the common denominator. Since 40 is just 20 doubled, and 20 is just 20 once, it fits into both numbers and is also the highest number that can fit.
Your customer has found base plates that are defective, they exceed the maximum width dimension of 4.005. As a result the mating component will not fit on these base plates properly. You manufacture these base plates on four identical CNC milling machines with approximately 25% of the production coming from each machine.
Simplified drawing of base plate is shown below.
Assignment:
Your manager has requested you sample 50 pieces from the manufacturing floor that were manufactured from each machine, analyze the data and come up with recommendations to solve the problem. (The data for the 50 piece sample is attached at the end of the assignment.)
Introduction: describing the process and statement of the general problem(s)
Analysis of the data: Graphical analysis is required
Each table and graph must be briefly explained at the point of the table or graph to indicate how it relates to the study at hand.
A brief summary of the findings relating back to specific analytical tools
Cause and effect diagram(s): identifying PERTINENT possible solutions to the problem(s)
The problem at hand involves base plates that exceed the maximum width dimension, resulting in improper fitting of the mating component. To address this issue, a sample of 50 base plates manufactured from each of the four CNC milling machines was analyzed.
Graphical analysis of the data revealed insights into the problem. Recommendations for solving the problem include identifying pertinent possible solutions through cause and effect diagrams.
The analysis of the sample data from each CNC milling machine provides valuable insights into the issue of base plates exceeding the maximum width dimension. By graphically analyzing the data, patterns or variations can be identified, helping to pinpoint the specific source of the problem. This analysis may involve creating graphs or tables to visualize the measurements and compare them across the machines.
To identify possible solutions, cause and effect diagrams, such as fishbone diagrams, can be utilized. These diagrams help to identify potential causes of the issue by categorizing them into different categories such as machine factors, material factors, human factors, and environmental factors.
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A scientist used a microscope to count the number of bacterial cells in a petri dish every hour.
Which function most accurately represents this data, where n is the number of bacteria and 1 is the time elapsed, in hours?
a. n=2t
b. n=2^t
c n=t^2
d. n=√t
Answer:
a. n=2t
Step-by-step explanation:
Given that
N denotes the number of bacteria
And, 1 denotes the time elasped in hours
Now based on this, the scientist used a microscope for counting the number of bacterial cells every hour
So,the function that represent correct data is
n = 2t
Therefore the correct option is A.
The same would be considered
plz answer I will mark brainlest
Answer:
(-3,0)
Step-by-step explanation:
y=-2x-6 and 2y=-4x-12
=-2x-6
Solution is
(-3,0)
Please help me in it! It's very difficult, i'm in 6th and I still don't understand this. Please, help me in this!!!
Answer:
40
where the line starts (75) and ends (115)
115-75=40
thats the quick way to solve... hope this helps!
Step-by-step explanation:
Brainliest?
Find the first five terms of the sequence defined by each of these recurrence relations and initial conditions
To find the first five terms of a sequence defined by a recurrence relation and initial conditions, we apply the relation repeatedly. Each term is calculated based on the previous terms in the sequence according to the given relation.
The first five terms of a sequence defined by a recurrence relation and initial conditions can be determined by applying the recurrence relation repeatedly. Each term is calculated based on the previous terms in the sequence, according to the given relation. Here are the first five terms for each recurrence relation:
1. Linear recurrence relation: If the recurrence relation is of the form an = an-1 + d, where "a" is the term and "d" is a constant, and the initial condition is a1 = c, then the first five terms can be found by adding the constant "d" repeatedly to the initial term "c". For example, if c = 2 and d = 3, the first five terms would be 2, 5, 8, 11, 14.
2. Quadratic recurrence relation: If the recurrence relation is of the form an = an-1² + c, where "a" is the term and "c" is a constant, and the initial condition is a1 = d, then the first five terms can be calculated by squaring the previous term and adding the constant "c". For instance, if d = 1 and c = 2, the first five terms would be 1, 3, 11, 123, 15187.
These examples demonstrate how to find the first five terms of a sequence by applying the given recurrence relation and initial conditions. By following the recurrence relation, each term is determined based on the previous terms in the sequence.
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MARKING BRAINLIST ASAPP pleaseee help
Answer:38
Step-by-step explanation:I think it's 38 because it said right 8 and down 15 so it's kinda like a grid right mean stay positive but also means it goes up so I did 45 plus 8 which is 53 minus 15 which is 38. Hope this gets brainliest
six and fifty-three hundredths as a decimal-
Yes, I'm D-U-M-B!
Answer:
6.58
Step-by-step explanation:
ahahahaha lol
Answer:
6.58
i hope this helps:)
Step-by-step explanation:
brainliest please?
Write the word sentence as an equation. Then solve the equation.
9 is the difference of a number n and 7.
An equation that represents this word sentence is
Answer: 9=n-7
Step-by-step explanation:
Please help !
50 points !
Use the quadratic regression feature of a graphing calculator to find a quadratic model. Round to the nearest hundredths place.
A. Y=0.06x^2+0.31+4
B. Y=-4.03x^2+0.32x+8.19
C. Y=0.06x^2-0.31x-4
D. Y=4.03x^2-0.32x-8.19
Answer:
It is A
Step-by-step explanation:
Answer:
its A he's right
Step-by-step explanation:
The proportion of students who fail the comprehensive statistics final had been 4%. With instruction moving completely online, instructors believe that this percentage will decrease for various reasons (the final must now be open book, some students will cheat, etc.). To test their claim, the appropriate test is
paired t test
z test for two proportions
t test for one mean
z test for one proportion
one-way ANOVA
The appropriate test to investigate whether the proportion of students failing the comprehensive statistics final has decreased with the shift to online instruction is the z test for two proportions.
Explanation:
The z test for two proportions is used when we want to compare two proportions or percentages from different populations or groups. In this case, we want to compare the proportion of students who fail the statistics final before and after the instruction moved online.
To conduct the z test for two proportions, we follow these steps:
1. Define the null hypothesis (H₀) and alternative hypothesis (H₁). In this case, the null hypothesis would be that the proportion of students failing the final is the same before and after the instruction moved online, while the alternative hypothesis would be that the proportion has decreased after the shift to online instruction.
2. Collect data on the number of students who fail the statistics final before and after the shift to online instruction.
3. Calculate the sample proportions for each group. Let's denote the proportion before the shift as p₁ and after the shift as p₂.
4. Calculate the standard error (SE) of the difference between two proportions using the formula:
SE = sqrt((p₁ * (1 - p₁) / n₁) + (p₂ * (1 - p₂) / n₂))
where n₁ and n₂ are the sample sizes for the two groups.
5. Calculate the test statistic (z) using the formula:
z = (p₁ - p₂) / SE
6. Determine the critical value for the desired significance level (e.g., 0.05) and compare it to the calculated test statistic. If the calculated test statistic falls within the critical region, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
7. Interpret the results and draw conclusions about whether there is sufficient evidence to support the claim that the proportion of students failing the statistics final has decreased after the shift to online instruction.
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Use the Linear Approximation to estimate Δꜰ=ꜰ(3.5)−ꜰ(3) ꜰᴏʀ ꜰ(x)=41+x2 (Use decimal notation. Give your answer to five decimal places.)
Δf≈ help (decimals)
Calculate the actual change.
(Use decimal notation. Give your answer to five decimal places.)
Δf = help (decimals)
Compute the error and the percentage error in the Linear Approximation.
(Use decimal notation. Give your answer to five decimal places.)
Error = help (decimals)
Percentage error = % help (decimals)
To estimate Δf = f(3.5) - f(3) using the linear approximation, we'll use the formula:
Δf ≈ f'(a) * Δx
where f'(a) represents the derivative of f at the point a, and Δx represents the change in the x-values.
Given that f(x) = 41 + [tex]x^2[/tex], we can calculate the derivative as:
f'(x) = 2x
Now, let's calculate the values step by step:
Calculate Δf:
Δf ≈ f'(a) * Δx
Δf ≈ f'(3) * (3.5 - 3)
Δf ≈ 2(3) * (3.5 - 3)
Δf ≈ 6 * 0.5
Δf ≈ 3
Calculate the actual change:
To calculate the actual change, we need to evaluate f(3.5) and f(3) separately:
f(3.5) = 41 +[tex](3.5)^2[/tex]
f(3.5) = 41 + 12.25
f(3.5) = 53.25
f(3) = 41 + [tex](3)^2[/tex]
f(3) = 41 + 9
f(3) = 50
Δf = f(3.5) - f(3)
Δf = 53.25 - 50
Δf = 3.25
Calculate the error and the percentage error:
Error = |Δf - Δf_approx|
Error = |3.25 - 3|
Error = 0.25
Percentage error = (|Δf - Δf_approx| / Δf) * 100
Percentage error = (0.25 / 3.25) * 100
Percentage error ≈ 7.69%
So, the results are as follows:
Δf ≈ 3
Actual change (Δf) ≈ 3.25
Error ≈ 0.25
Percentage error ≈ 7.69%
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Answer ASAP pls pls
Answer:
67.5
Step-by-step explanation:
b times h
7.5 times 9
Answer:
A = 67.5 in²
Step-by-step explanation:
The area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the perpendicular height )
Here b = 9 and h = 7.5 , then
A = 9 × 7.5 = 67.5 in²
1 Consider a tournament between N teams, each team playing each of the other teams. We can represent the results of this tournament by a directed graph: node i represents team i, and an edge exists i+jif team i beat team j. The above problem suggests that it may be impossible to declare an absolute winner, as everyone may be beaten by somebody. We could relax this slightly in the following way: let's call team i a k-winner if there is a group of k-many teams that were each beaten by team i. Other teams may have beaten team i, but there is at least a group of size k that was roundly beaten by i. 3) If the results of each game are decided by fair coin flip, what is the probability that a given team i is a k-winner? (5 points) 4) Using result 3.0, bound the probability that there exists a k-winner in a tournament of size N? Write it nicely as you can but don't beat yourself up too much with it. (5 points) 5) For N = 100, what is the smallest k that 3.4 indicates the probability of having k-winners is less than 1? Code or Mathematica to evaluate your answer in 3.4 is fine. (5 points) 6) For N = 100 and k as in 3.5, argue that there exist possible tournaments with no k-winners. (5 points) Bonus: Using the Chernoff bound to bound the relevant probabilities, show that for a > 1/2 the probability of there being any oN-winners goes to 0 as No. Conclude therefore that there erist tournaments without a N-winners, for all sufficiently large N. (10 points)
The analysis involves calculating probabilities, bounding the probabilities based on worst-case scenarios, and considering the implications of the Chernoff bound to demonstrate the existence of tournaments without a certain number of winners.
In a tournament between N teams, where each team plays each other, the concept of a k-winner is introduced. A team i is considered a k-winner if there is a group of k teams that were each beaten by team i. The probability that a given team i is a k-winner can be calculated when the results of each game are decided by a fair coin flip. This probability depends on the number of teams and the specific value of k.
Using this probability for a given team, we can bound the probability that there exists a k-winner in a tournament of size N. This bound takes into account the probabilities of individual teams being k-winners and considers the worst-case scenario.
For a specific value of N, such as N = 100, we can determine the smallest k for which the probability of having k-winners is less than 1. This can be done by evaluating the probabilities for different values of k until the desired condition is met.
When N = 100 and k is determined as in the previous step, it can be argued that there exist possible tournaments with no k-winners. This can be demonstrated by constructing specific scenarios or by analyzing the probabilities of different outcomes.
Using the Chernoff bound, it can be shown that for a value a greater than 1/2, the probability of having any oN-winners (where oN is an arbitrary constant) goes to 0 as N approaches infinity. This conclusion implies that there exist tournaments without N-winners for sufficiently large values of N.
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Gerry conversed his sole partnership to an S corporation and transferred several assets to the corporation. The assets cost $19,570 and had an adjusted basis of $9,600. He also spent an additionally $975 to make the conversion to an S corporation. What is his beginning basis in the S corporation?
Gerry's beginning basis in the S corporation is $20,545.
To calculate Gerry's beginning basis in the S corporation, we need to consider the cost of the assets transferred and the additional expenses incurred for the conversion.
The cost of the assets transferred is given as $19,570. This represents the original cost of the assets when Gerry acquired them.
The adjusted basis of the assets is stated as $9,600. The adjusted basis takes into account any adjustments made to the original cost, such as depreciation or other deductions.
To calculate the beginning basis in the S corporation, we add the cost of the assets transferred ($19,570) to the adjusted basis ($9,600). This gives us a total of $29,170.
In addition to the assets, Gerry incurred an additional expense of $975 for the conversion to an S corporation. We include this amount in the calculation of the beginning basis.
Therefore, Gerry's beginning basis in the S corporation is $29,170 + $975 = $20,545.
This beginning basis is important for determining Gerry's tax consequences and future deductions within the S corporation structure.
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The quotient of a number more than 1 and 3 is 5
Answer:
https://brainly.com/question/13518166
Step-by-step explanation:
find the buying price if the selling price is 240 and profit is 20 percent
Answer:
192
Step-by-step explanation:
You have to find 20% of 240.
So write 20% as 20 over 240 in fraction form.
[tex]\frac{20}{240}[/tex]
Since, finding the fraction of a number is same as multiplying the fraction with the number, we have
[tex]\frac{20}{100}[/tex] of 240 = [tex]\frac{20}{100}[/tex] × 240
Therefore, the answer is 48
If you are using a calculator, simply enter 20÷100×240 which will give you 48 as the answer.
Now since it wants to know how much you paid for the goods you do 240-48=192
So since a company is selling goods with a 20% profit
That means they bought it from somewhere else
Because they had to be manufactured
It wants how much the company paid the company that manufactured the goods
I hope this helped. Some resources that are helpful to look at in case of any more confusion are:
https://answers.everydaycalculation.com/percent-of/20-240
https://www.mathsisfun.com/
https://www.ixl.com/
Good luck young mathematician!
A certain airplane offers two types of seats, first class and economy.
There are 209 total seats on the airplane. If the difference between the
number of economy and first class seats is 153, find the number of
economy seats.
Answer:
56
Step-by-step explanation:
you do 209-153=56
Number of economy seats are 181
What is linear equation?An equation between two variables that gives a straight line when plotted on a graph
Consider,
Number of economy seats =x
Number of First class seats =y
There are 209 total seats on the airplane
Then,
x + y=209
Difference between the number of economy and first class seats is 153
x - y=153
Solve both the equation
x + y=209
x = 209-y
Substitute the value of x in second equation
(209-y) - y=153
2y=209-153=56
y=28
Then
x + y=209
x + 28=209
x=209-28
x=181
Hence, the number of economy seats are 181
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please helpppp which function h(x) results when g(x) is translated 7pi/8 units right and one unit down????
Answer:
The second option
Step-by-step explanation:
please help please it would me me sm <3
Answer:
25
Step-by-step explanation:
4x25=100
100-25=75 degrees
Answer:
25°
Step-by-step explanation:
(4x-25)=75
4x=100
x=25
What is k^2+16k+64+89
Answer:
k²+16k+ 153
Step-by-step explanation:
k²+16k+64+89
= k²+16k+ 153
A bottling company uses a filling machine to fill plastic bottles with cola. The bottles are supposed to contain 300 milliliters (ml). In fact, the contents vary according to a Normal distribution with mean μ=298ml and standard deviation σ=3ml. What is the probability that the mean contents of six randomly selected bottles are less than 295 ml?
The probability that the mean contents of six randomly selected bottles are less than 295 ml is 0.007, or 0.7%.
To find the probability that the mean contents of six randomly selected bottles are less than 295 ml, we can use the Central Limit Theorem. According to the Central Limit Theorem, the distribution of sample means from a population with any distribution approaches a normal distribution as the sample size increases.
In this case, we have a normal distribution with a mean (μ) of 298 ml and a standard deviation (σ) of 3 ml. We want to find the probability of the mean contents of six bottles being less than 295 ml.
First, we need to calculate the standard error of the mean, which is the standard deviation of the sampling distribution of the mean. The formula for the standard error is σ / √n, where σ is the population standard deviation and n is the sample size.
In our case, σ = 3 ml and n = 6. Therefore, the standard error (SE) is:
SE = 3 / √6 ≈ 1.225 ml
Next, we need to calculate the z-score, which is the number of standard errors the sample mean is away from the population mean. The formula for the z-score is (x - μ) / SE, where x is the sample mean.
In our case, x = 295 ml, μ = 298 ml, and SE = 1.225 ml. Therefore, the z-score is:
z = (295 - 298) / 1.225 ≈ -2.449
Finally, we can use a standard normal distribution table or a calculator to find the probability corresponding to the z-score. The probability that the mean contents of six bottles are less than 295 ml is the area under the normal curve to the left of the z-score.
Using a standard normal distribution table or calculator, we find that the probability corresponding to a z-score of -2.449 is approximately 0.007.
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Find the volume of the cylinder. Use 3.14 for T.
height of 3 radius of 3
Answer:
84.82
Step-by-step explanation:
π·32·3≈84.823
Answer:
The volume of a cylinder with a height of 3 and a radius of 3 is 84.823 or you could say 84.8.
Step-by-step explanation:
How do I solve for the missing side lengths. My sender has to be as a radical in simplest form.
Answer: 6√6
Step-by-step explanation: When an angle is 45 degrees in a triangle it is actually half a square (I know right!!!), so, therefore, the other side length will also be 6, and then using the Pythagorean theorem we get the hypotenuse to be 6√2. Now, when an angle is 60 degrees in a triangle it is actually half an equilateral triangle (I know right!!!), so, therefore, the other side length will be double the length, 12√2, and using the Pythagorean theorem we get the side length x to be 6√6! Hope this helps!
find the slope. -2,1 and 4,4
Answer:
2
Step-by-step explanation:
To find the slope of two points, we must subratct the Y values from each other and divide them from the X values
4-(-2) 6
--------- = ----- = 2
4-1 3
Answer: The slope is 1/2 as a fraction and 0.5 as a decimal
Hope it helped :D
Please please help please please ASAP ASAP please ASAP help please please ASAP please please help ASAP ASAP please please help please please ASAP please
Answer:
7
Step-by-step explanation:
The two lengths (4x-7 and x+14) are the same. This is because if we look at the big trapezoid as a whole, the ratio of the three segments on the side (4, 4, 4) is the same as the ratio of the three lengths on the other side. Therefore the ratio of the two lengths would be the same as well, 1:1. (btw the photo that I attached is what I mean by the two sides). So, we can form the equation: 4x-7 = x+14. The steps to solve the problem:
4x-7 = x+14
3x=21
x=7
The value of x is 7!
[tex] \sqrt{39} [/tex]
Please help me to find the answer of square root 39
plz
Answer:
hi dear friend the answer is 6.245. hope that helps it has been a pleasure to help you can always look out for me if you have a math problem.
Jim and three friends shared 2 poster boards for an art project. What part of the construction paper will each friend get? *
Answer: 1/2 of a sheet
Step-by-step explanation:
2 sheets divided by 4 people
2/4
Simplify to 1/2
Calculate the integral ∫ [(1+cos(arctan (3x))+(arctan (3x))^5)/(1+9x^2]dx.
The solution of the integral (1/6)ln|9x²+1| +(1/3)arctan (3x) +(1/6)arctan((3x)²)- (1/18)(3x)²/(9x²+1) + (1/90)(3x)⁴/(9x²+1) + C.
We have the following integral to solve.∫ [(1+cos(arctan (3x))+(arctan (3x))⁵)/(1+9x²2)]dx
Let's begin by using the substitution u = arctan(3x).
We need to convert this integral into a U-form. By substituting the above expression, we have the following new expression.
∫ [(1+cos u)+u⁵]/[1+9(3tanu)²] *(1/3) du=∫ [(1+cos u)+u⁵]/(9tan²u+1) *(1/3) du
Let's now consider the numerator.
We have 1+cosu+u⁵ in the numerator. Let's break down the integral into 3 parts. The first part is ∫(1)/(9tan²u+1) *(1/3) du.
We can convert the denominator to a perfect square of the form 3²tan²u+1 which simplifies to (3tanu+1)(3tanu-1)+2.
Let's now factorize
= ∫(1)/(9tan²u+1) *(1/3) du
=∫(1)/[(3tanu+1)(3tanu-1)+2] *(1/3) du
Now let's perform partial fraction decomposition. We have 1/[(3tanu+1)(3tanu-1)+2] which we can write as
= A/(3tanu+1)+B/(3tanu-1)+C/(3tan²u+1) where A, B, and C are constants to be determined.
We now have 1= A(3tanu-1)(3tan²u+1)+ B(3tanu+1)(3tan²u+1)+ C(3tanu+1)(3tanu-1).
Let's now set up the system of equations.
The first equation is
1= A(3tanu-1)(3tan²u+1)+ B(3tanu+1)(3tan²u+1)+ C(3tanu+1)(3tanu-1)
Putting u=0, we get
A = 1/4
Putting u =pi/3, we get
B=1/4 Putting
u = arctan(1/√(3)), we get C=1/2. Now that we have A, B, and C, let's substitute them back to our integral.
We have
= ∫(1)/[(3tanu+1)(3tanu-1)+2] *(1/3) du
= (1/4)∫(1)/(3tanu+1) du + (1/4)∫(1)/(3tanu-1) du +(1/2)∫(1)/(3tan²u+1) du
Let's now solve the integral and simplify.
= ∫(1)/(3tanu+1) du
= (1/6)ln|3tanu+1|- (1/6)ln|3tanu-1|+ (1/3)arctan (3tanu).
Similarly,
= ∫(1)/(3tanu-1) du
= (-1/6)ln|3tanu+1|+ (1/6)ln|3tanu-1|+ (1/3)arctan (3tanu).
The third integral we can solve by substitution
v = √(3)tanu.
We then get
= ∫(1)/(3tan²u+1) du= (1/√(3))∫(1)/(v²+3) dv
= (1/sqrt(3))arctan(v/√(3))
= (1/√(3))arctan((√(3)tanu)/√(3)).
We can now put back all the values to get the solution.
= ∫ [(1+cos(arctan (3x))+(arctan (3x))⁵)/(1+9x²)]dx
= (1/3)∫ [(1+cos u)+u⁵]/(9tan²u+1) du
=(1/3)[(1/4)(ln|3tanu+1|- ln|3tanu-1|+ 2arctan (3tanu))+(1/4)(-ln|3tanu+1|+ ln|3tanu-1|+ 2arctan (3tanu))+(1/2)(1/√(3))(arctan((sqrt(3)tanu)/√(3)))]+ C
We can simplify the above expression to get
=- ∫ [(1+cos(arctan (3x))+(arctan (3x))^5)/(1+9x²)]dx
= (1/6)ln|9x²+1| +(1/3)arctan (3x) +(1/6)arctan((3x)²)- (1/18)(3x)²/(9x²+1) + (1/90)(3x)⁴/(9x²+1) + C
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1. The values, x in a sample of 15 are summarized as follows
Σ(x-c) = 72,Σ(x-c)2 = 499.6
where c is a constant. Given that the sample mean is 104.8.
(a) Find the value of constant c.
(b) Find the variance of x.
Answer:
(a) 100
(b) 10.27
Step-by-step explanation:
We are given
No of elements = 15
Σ(x-c) = 72,Σ(x-c)^2 = 499.6
,where c is a constant
and the sample mean is 104.8.
(a) lets take into account Σ(x-c) = 72
this means that we have the sum of the 15 elements of x and each element of x is subtracted by the constant c
so the equation becomes Σxi -15c = 72, ............(1)
where xi means the sum of the elements of x from 1 to 15.
we are given the mean as 104.8
this means that Σxi/15 = 104.8
Σxi = 15*104.8 = 1572 .............(2)
substituting (2) in (1)
we get
1572 - 15c = 72
15c = 1500
c = 100
(b) We will use the property that variance does not change when a constant value is added or subtracted to the elements. This we can observe in the given equation that c is a constant that has the value of 100.
so the variance is
σ^2 = Σ(x-c)^2/15 - (Σ(x-c)/15 )^2
= 499.6/15 - (72/15)^2
= 33.31 - 23.04
σ^2 = 10.27
Therefore the variance of the given problem is 10.27.