On this problem, the answer has been worked out, but you must fill in the blanks in the solution.A study of carbon monoxide deaths showed that a random sample of 6 recent years had a standard deviation of 4.1 deaths per year. Find the 99% confidence interval of the variance and the standard deviation. Round answers to the nearest tenth (one digit after the decimal point).Solution: We are finding confidence intervals for the variance and standard deviation, so we use the formulas
Answers
You have to calculate the confidence interval for the population variance and population standard deviation of carbon monoxide deaths.
To calculate the confidence interval for the population variance you have to use the following formula, which is derived from the Chi-Square distribution:
[tex]\lbrack\frac{(n-1)S^2}{\chi^2_{n-1;1-\frac{\alpha}{2}}};\frac{(n-1)S^2}{\chi^2_{n-1;\frac{\alpha}{2}}}\rbrack[/tex]For a sample of n=6 years, the sample standard deviation is S=4.1 deaths per year
To calculate the interval, the first step is to determine the values under the Chi-Square distribution with n-1 degrees of freedom and a confidence level of 0.99
The degrees of freedom for this particular distribution is:
[tex]n-1=6-1=5[/tex]The confidence level is 0.99, calculate the value of α:
[tex]\begin{gathered} 1-\alpha=0.99 \\ \alpha=1-0.99 \\ \alpha=0.01 \end{gathered}[/tex]For the chi-Square value of the left bound, the value of probability is
[tex]1-\alpha/2=1-0.01/2=1-0.005=0.995[/tex]The Chi-Square value for the left bound of the interval corresponds to a distribution with 5 degrees of freedom and 0.995 of accumulated probability
[tex]\chi^2_{5;0.995}=16.8[/tex]So the value of the distribution for the left bound is χ²left= 16.8
For the right bound of the interval, the accumulated probability under the distribution is α/2
[tex]\frac{\alpha}{2}=\frac{0.01}{2}=0.005[/tex]The Chi-Square value for the right bound of the interval is for distribution with 5 degrees of freedom and 0.005 accumulated probability:
[tex]\chi^2_{5;0.005}=0.412[/tex]The value of the distribution for the right bound is χ²right= 0.412
The sample variance is equal to the square of the sample standard deviation so that:
[tex]\begin{gathered} S^2=4.1^2 \\ S^2=16.81 \end{gathered}[/tex]Now you can calculate the confidence interval as follows:
Left bound of the interval
[tex]\frac{(n-1)S^2}{\chi^2_{5;0.995}}=\frac{(6-1)16.81}{16.8}=5.00[/tex]Right bound of the interval
[tex]\frac{(n-1)S^2}{\chi^2_{5;0.005}}=\frac{(6-1)16.81}{0.412}=204.00[/tex]The calculation of the interval can be written as follows:
[tex]\frac{(6-1)4.1^2}{16.8}\leq\sigma^2\leq\frac{(6-1)4.1^2}{0.412}[/tex]So, using a 99% confidence level, the interval for the population variance of the carbon monoxide deaths is [5.00;204.00] deaths per year²
Finally, apply the square root to both bounds of the interval to determine the confidence interval for the population standard deviation:
[tex]\begin{gathered} \sqrt[]{\frac{(6-1)4.1^2}{16.8}}\leq\sigma\leq\sqrt[]{\frac{(6-1)4.1^2}{0.412}} \\ \sqrt[]{\frac{5\cdot16.81}{16.8}}\leq\sigma\leq\sqrt[]{\frac{5\cdot16.81}{0.412}} \\ 2.236\leq\sigma\leq14.283 \\ \end{gathered}[/tex]Rounding to the nearest tenth the interval can be expressed as follows
[tex]2.2\leq\sigma\leq14.3[/tex]Using the same confidence level the confidence interval for the population standard deviation is [2.2;14.3] deaths per year.
Related Questions
Find the area of the shaded sector QRS
Answers
The diagram given is a sector, and from the diagram
Radius(r) = 9 in
[tex]\theta=120^{\cdot}[/tex][tex]\begin{gathered} \text{Area of a sector = }\frac{\theta}{360}\times\pi r^2 \\ \\ \text{Area of a sector = }\frac{120}{360}\times\frac{22}{7}\times9^2 \\ \text{Area of a sector =}\frac{19440}{2520}=7.71in^2 \end{gathered}[/tex]Find the values of x and y to make the following numbers equal
Answers
If all numbers has to be equal, that means:
[tex]\begin{gathered} \frac{-2}{x}=-0.2 \\ \frac{y}{5}=-0.2 \end{gathered}[/tex]Let's solve the value of x and y that makes the equation above equal. Let's start with x.
[tex]\begin{gathered} \frac{-2}{x}=-0.2 \\ \text{Cross multiply.} \\ -2=-0.2x \\ \text{Divide -0.2 on both sides.} \\ \frac{-2}{-0.2}=\frac{-0.2x}{-0.2} \\ 10=x \end{gathered}[/tex]The value of x is 10.
Let's solve for y.
[tex]\begin{gathered} \frac{y}{5}=-0.2 \\ \text{Cross multiply.} \\ y=-1 \end{gathered}[/tex]The value of y is -1.
13 In August, 85% of the middle school students voted in a school election. The number of students who voted was 544.
How many students are in the middle school?
(A) 462 students
(B) 544 students
(C)629 students
(D) 640 students
Answers
Answer:
D. 640 students
Step-by-step explanation:
hope this helps
3) Given the points (6-11) and (-2,9), find the following: a) find the slope between these points, b) find the equation of the line between these points, b) find the y-intercept of this line, c) graph this line.
Answers
Points (6,-11) and (-2,9)
then
a) Slope m= Y/X = (9 --11)/ (-2-6) = 20/-8= -5/2
b) equation of line y = mx + b
find b= y - mx = 9 -(-5/2)•(-2) = 9 - 5= 4
then equation is
y= (-5/2)x + 4
c) y-intercept of this line is
x= 0 , y= 4
d) graph of this line
What is the Area of a circle with the radius of 5
Answers
Answer:
Answer is 78.5
Step-by-step explanation:
the formula for the Area of a cirlcle is [tex]\pi[/tex][tex]r^{2}[/tex]
using it:
area = 3.14 * 5^2
area = 78.5
Write the coordinate point for the vertex of this parabola: 1,2 x=
Answers
Given:
[tex]x=-\frac{1}{8}y^2[/tex]Vertex of the parabola is (0,0).
The triangles in the figure below are similar.
image b125a080d0e9444e9eebf9b6644403df
Which proportion is correct?
A.
x20=96
x
20
=
9
6
B.
x20=915
x
20
=
9
15
C.
2015=x6
20
15
=
x
6
D.
x20−x=156
x
20
−
x
=
15
6
Answers
The proportion that is correct to find the value of x in the similar triangles is: B. x/20 = 9/15.
What are Similar Triangles?For any two triangles that are similar to each other, their corresponding sides will have lengths that are proportional to each other, which means they have the same ratio.
The triangles as shown in the image attached below are said to be similar to each other, this means they have side lengths that are proportional to each other or their corresponding sides will have proportional lengths.
Therefore, we will have the following proportion if we intend to find the value of x in the image given:
x corresponds to 20 while 9 corresponds to the side that measures (9 + 6) 15.
Therefore, the correct proportion is:
x/20 = 9/15.
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-4(x-1) I forgot how to simplify it
Answers
Answer:
Step-by-step explanation:
-4(x-1)
distribute the -4
-4x + 4
help me with this im really confused lol please
Answers
Answer:
Here is the equation in quadratic form:
x= 3±i√47/4
Highlighter
Clear
At the grocery store, three brands of raisin bran are sold. For Brand A, the equation y = 0.18x represents
the cost, y, of x ounces of raisin bran. For Brand B, the table shows the amounts paid for different
amounts of raisin bran. For Brand C, the graph shows the relationships between the total cost, y, and the
number of ounces of raisin bran, x.
Amount of
Raisin Bran
(ounces)
0
10
24
Brand B
27
Total Cost
(dollars)
0
1.60
3.84
4.32
Total Cost (dollars)
4
Brand C
Answers
Answer: brand A 0.21 0.18 brand B brand c 0.16
Step-by-step explanation:
find the error & explain why it is wrong: jon had to solve the equation below. what did he do wrong?
Answers
Answer:
Step B is incorrect because the factors of [tex]x^2 + 4x + 3[/tex] should be:
[tex](x + 3)(x + 1)[/tex]
The perimeter of the quadrilateral ABCD is 105 inches
what is the Lenght of segment BC
Answers
Answer:
Hello, I would need to see an image of the quadrilateral at hand to be able to answer your question.
Step-by-step explanation:
Just let me know, here to help!
4.* 4. Students were asked how many hours a weeknight they spend on homework and exercise. The dot plots display the results. Which statement is not supported? Homework Exercise LG 2 3 4 5 Number of Hours 1 2 3 4 5 Number of Hours A. More time is spent on homework than exercise. B. The mode activity times are equal. C. The median exercise time is not equal to the median homework time. D. The range of homework hours is greater for homework than for exercise ОА
Answers
Analyze each statement to see if it is supported by the dot plots or not.
A) More time is spent on homework than exercise.
Find the total time spent on each activity to compare
What is the slope of this line?
A. - 1/3
B. 1/3
C. 2/3
D. - 2/3
Answers
Answer:
2/3
Step-by-step explanation:
rise/run=slope
2 up and 3 to the right to it is 2/3
How to substitute 8x-4y=-12, 8x+y=-17
Answers
we have the system
8x-4y=-12 -----> equation A
8x+y=-17 -----> y=-17-8x -----> equation B
substitute equation B in equation A
8x-4(-17-8x)=-12
solve for x
8x+68+32x=-12
40x=-12-68
40x=-80
x=-2
Find the value of y
y=-17-8(-2)
y=-17+16
y=-1
the solution is x=-2y=-1Example8x-4y=-12 -----> equation A8x+5y=-17 -----> equation B
isolate the variable y in equation B (or equation A)
5y=-17-8x
y=-(17/5)-(8/5)x
substitute in equation A
8x-4[-(17/5)-(8/5)x ]=-12
solve for x
10 points and brainliest to first correct answer! please answer both!
Answers
An explicit formula for the sequence -2,3,8,13,18 is aₙ = 7 - 5n.
The express method for a mathematics collection is an = a + (n - 1)d, and any time period of the collection can be computed, without knowing the opposite terms of the collection. In preferred, the explicit method is the nth time period of mathematics, geometric, or harmonic sequence.
Calculation:-
a₁ = 2
a₂ = 2 - 5 = -3
a₃ = -3 - 5 = -8
a₄ = -8 -5 = -13
a₅ = -13 -5
= -18
The formula for the nth term of explicit sequence is aₙ = a₁ +(n - 1)d
where a₁ = 2 and d = 5
So,
aₙ =2 + (n - 1)(-5) using distributive property
aₙ = 2 + n (-5)+(-1)(-5)
aₙ = 2 - 5n + 5
aₙ = 7 - 5n
The explicit formulae for L-capabilities are members of the family between sums over the complicated variety zeroes of an L-characteristic and sums over prime powers, introduced by Riemann for the Riemann zeta feature.
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. Julia is buying vegetables at a
farmer's market. One of the stands is
selling zucchini for $1.25 per pound.
The total weight of the zucchini she
has selected is 3.8 pounds. How
much will she pay for
Answers
Answer:
$4.75
Step-by-step explanation:
We can use a simple multiplication statement to solve this problem.
3.8 × 1.25 = 4.75
true or flase? Any method (elimination, substitution, or graphing) can be used to any possible system of linear equations.
Answers
Answer:
Step-by-step explanation:
Yes, you can use either the system of elimination, substitution, or graphical method to solve linear equations
hello I seem to be having issues on this problem
Answers
Okay, here we have this:
Considering the provided data set, we are going to create the corresponding histogram, so we obtain the following:
The above histogram corresponds to the one requested in the exercise.
PLEASE HELP I GOT LIKE 15 MINUTES LEFT
One small circle is completely inside a larger circle. Both circles share the same center point. Calculate the area of the shaded region.
Answers
Answer:
133π square centimeters
Step-by-step explanation:
Area of larger circle:
[tex]\pi( {13}^{2} ) = 169\pi[/tex]
Area of smaller circle;
[tex] \pi( {6}^{2} ) = 36\pi[/tex]
Area of shaded region:
[tex]169\pi - 36\pi = 133\pi[/tex]
On average, Logan drinks 3/4 of a 12-ounce glass of water in 1 3/4 hours. How many glasses of water does he drink in one hour? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.
Answers
Answer:
4.5 ounce or 3/4 of 6-ounce glass.
Step-by-step explanation:
I don't know -_- I'm too lazy for this.
Draw a tree diagram to solve the following question.A bag contains 5 red and 3 blue marbles. Two marbles are drawn simultaneously from thebag. Determine the probability that at least one is red.
Answers
Step 1. There are 5 red marbles and 3 blue marbles, 8 marbles in total:
Step 2. Two marbles are drawn simultaneously, which means that there is no replacing of the marbles.
To make the tree diagram with the probabilities for each marble, remember the probability formula:
[tex]P=\frac{\text{Number of favourable outcomes}}{total\text{ numer of outcomes}}[/tex]The three will look as follows:
For the first marble, the probability of getting a red one is 5/8 because there are 5 red marbles out of a total of 8, and similar to the first one is blue.
For the second marble, we consider that the total number of marbles is now 7.
Step 3. To find the probability of each combination, we multiply the values of each branch:
The results of the multiplications is:
The ones that have at least one red marble are the first three branches: red-red, red-blue, and blue-red.
To find the probability of at least one red marble, we add the results of the first three branches:
[tex]\frac{20}{56}+\frac{15}{56}+\frac{15}{56}[/tex]The result is:
[tex]\frac{20}{56}+\frac{15}{56}+\frac{15}{56}=\frac{50}{56}[/tex]The probability is 50/56.
The fraction can be simplified to:
[tex]\frac{50}{56}=\frac{25}{28}[/tex]The probability simplified is 25/28.
Answer:
[tex]\frac{25}{28}[/tex]Find the value of √√441 + √16 + √4
Answers
Answer:
Your answer would be 10.582575695, the rounded answer would be 10.60.
Step-by-step explanation:
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
4) =√7√ and =√63√ where and are poitive integer. Given that :=1:9 find, in it implet form, the ratio :
Answers
The ratio of a and b in the simplest form is a:b = 1:3 .
In the question ,
it is given that ,
a = √7 + √c and
b = √63 + √d
and the ratio of c and d is given as c : d = 1 : 9 , which means c/d = 1/9
on cross multiplication , we get
d = 9c
Substituting d=9c in the equation b = √63 + √d ,
we get ,
b = √63 + √9c
b = 3√7 + 3√c
taking 3 common , we get
b = 3(√7 + √c)
b = 3a ......because a = √7 + √c .
b/a = 3/1
So, a/b = 1/3
the ratio is a:b = 1:3 .
Therefore , The ratio of a and b in the simplest form is a:b = 1:3 .
The given question is incomplete , the complete question is
If a = √7 + √c and b = √63 + √d , where c and d are positive integers. Given that c : d = 1 : 9 . find, in its simplest form, the ratio a : b ?
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Which statement is true regarding the graphed functions? 8 6 4 -6-5-4-3-2 436 - -6 1979 - 2 -127 (0) = g(0) 1-2) = g(-2) f(0) = g(-2)
Answers
Let's check the choices one by one.
From the figure,
Choice A :
f(0)=g(0)
f(0) = -2
g(0) = -2
So f(0) = g(0) is true!
Choice B :
f(-2) = g(-2)
f(-2) = 4
g(-2) = -4
So f(-2) = g(-2) is false!
Choice C:
f(0) = g(-2)
f(0) = -2
g(-2) = -4
So f(0) = g(-2) is false!
The correct answer is Choice A. f(0) = g(0)
The length of the base of an isosceles triangle is x. The length of a leg is 2x-3. The perimeter of the triangle is 19. Find x
Answers
Step-by-step explanation:
isoceles means that the triangle has 2 equally long legs.
the perimeter is the sum of all sides.
so,
19 = x + (2x - 3)×2 = x + 4x - 6 = 5x - 6
25 = 5x
x = 5
Peter has $ 40 to spend on rides at the state fair. Each ride costs $3. Find the recursiveand the explicit function.Recursive Function:Explicit Function:
Answers
Recursive function: f(n) = f(n-1) + 3
Explicit function: f(n) = 3n
Explanations:Amount of money Peter has to spend = $40
Cost of each ride = $3
Let the number of rides be represented as n
The recursive function is a function in which each term always depends on the preceding terms. In this case, Peter pays $3 after every ride. This means that he adds 3 to every preceding amount that he spends on the rides.
The recursive function is therefore:
f(n) = f(n-1) + 3
The explicit function: This function is always expressed in a clear form (i.e. explicitly)
3 x number of rides = Amount spent
The explicit function is therefore:
f(n) = 3n
The activity preference of teachers and librarians is given in the table.
Teachers Librarians
Movies 3 12
Books 4 9
Plays 2 15
Based on the information in the table, which of the following is an example of independent events.
P(librarian and chooses book)
P(librarian and chooses movie)
P(teacher and chooses play)
P(teacher and chooses book)
Answers
The activity preference of teachers and librarians is given in the table. P(teacher and chooses play) is an example of an independent event.
What is an independent event?An independent event is an activity whose occurrence does not depend on other events.For example, if a coin is tossed and the result is heads, tossing the coin again will result in tails. In both cases, the occurrence of both events are independent of each other. This is one type of activity in probability. Learn here the full definition of independent events and how they differ from Venn diagrams, examples, and mutually exclusive activity .In probability theory, the set of outcomes of an experiment is called an event. There are different types of events, including independent events, dependent events, and mutually exclusive events.A and B are said to be independent events if the probability of an event A occurring is unaffected by the occurrence of another activity B.To learn more about independent event from the given link :
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help meeeeeeeeeeeeeeeeeeee pleaseee rnnnn rn!!!!
Answers
The length of the bar is 10.5 foot and the width of the bar is 5.7 foot .
In the question ,
it is given that
the base area of the large chocolate bar is 59.85 square foot .
let the length of the chocolate bar be "l"
and the breadth of the chocolate bar be "b"
given that the length is 0.9 foot shorter than twice its width , means
l = 2w - 0.9
we have the area of rectangle = length [tex]\times[/tex] width
Substituting the values of length , width and area we get
59.85 = (2w - 0.9 ) * w
59.85 = 2w² - 0.9w
2w² -0.9w -59.85 = 0
On solving the quadratic equation ,
we get w = -5.25 and w = 5.7
width cannot be in negative , so, the width is 5.7 foot .
and l = 2(5.7) -0.9 = 11.4 - 0.9 = 10.5
Therefore , the length of the bar is 10.5 foot and the width of the bar is 5.7 foot .
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The softball team at west river middle school needs New Jersey’s and new hats . A Jersey costs $40 , and a hat costs $15 . The softball team has a total of $1,200 to spend . Let x equal the number of jersey’s the team orders and y equal the number of hats the team orders. Which inequality models this situation
Answers
The inequality model will be 40*x + 15*y ≤ $1200.
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
The given information, cost of a Jersy = $40
Cost of Hat = $15
The softball team has a total of $1,200 to spend.
Let x equal the number of jersey’s the team orders and y equal the number of hats the team orders.
So the total money will be spend within the budget will be
40*x + 15*y ≤ $1200
Hence, the inequality model will be 40*x + 15*y ≤ $1200.
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