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Complete Question
At one point the average price of regular unleaded gasoline was $3.39 per gallon. Assume that the standard deviation price per gallon is $0.07 per gallon and use Chebyshev's inequality to answer the following.
(a) What percentage of gasoline stations had prices within 3 standard deviations of the mean?
(b) What percentage of gasoline stations had prices within 2.5 standard deviations of the mean? What are the gasoline prices that are within 2.5 standard deviations of the mean?
(c) What is the minimum percentage of gasoline stations that had prices between $3.11 and $3.67?
Answer:
a) 88.89% lies with 3 standard deviations of the mean
b) i) 84% lies within 2.5 standard deviations of the mean
ii) the gasoline prices that are within 2.5 standard deviations of the mean is $3.215 and $3.565
c) 93.75%
Step-by-step explanation:
Chebyshev's theorem is shown below.
1) Chebyshev's theorem states for any k > 1, at least 1-1/k² of the data lies within k standard deviations of the mean.
As stated, the value of k must be greater than 1.
2) At least 75% or 3/4 of the data for a set of numbers lies within 2 standard deviations of the mean. The number could be greater.μ - 2σ and μ + 2σ.
3) At least 88.89% or 8/9 of a data set lies within 3 standard deviations of the mean.μ - 3σ and μ + 3σ.
4) At least 93.75% of a data set lies within 4 standard deviations of the mean.μ - 4σ and μ + 4σ.
(a) What percentage of gasoline stations had prices within 3 standard deviations of the mean?
We solve using the first rule of the theorem
1) Chebyshev's theorem states for any k > 1, at least 1-1/k² of the data lies within k standard deviations of the mean.
As stated, the value of k must be greater than 1.
Hence, k = 3
1 - 1/k²
= 1 - 1/3²
= 1 - 1/9
= 9 - 1/ 9
= 8/9
Therefore, the percentage of gasoline stations had prices within 3 standard deviations of the mean is 88.89%
(b) What percentage of gasoline stations had prices within 2.5 standard deviations of the mean?
We solve using the first rule of the theorem
1) Chebyshev's theorem states for any k > 1, at least 1-1/k² of the data lies within k standard deviations of the mean.
As stated, the value of k must be greater than 1.
Hence, k = 3
1 - 1/k²
= 1 - 1/2.5²
= 1 - 1/6.25
= 6.25 - 1/ 6.25
= 5.25/6.25
We convert to percentage
= 5.25/6.25 × 100%
= 0.84 × 100%
= 84 %
Therefore, the percentage of gasoline stations had prices within 2.5 standard deviations of the mean is 84%
What are the gasoline prices that are within 2.5 standard deviations of the mean?
We have from the question, the mean =$3.39
Standard deviation = 0.07
μ - 2.5σ
$3.39 - 2.5 × 0.07
= $3.215
μ + 2.5σ
$3.39 + 2.5 × 0.07
= $3.565
Therefore, the gasoline prices that are within 2.5 standard deviations of the mean is $3.215 and $3.565
(c) What is the minimum percentage of gasoline stations that had prices between $3.11 and $3.67?
the mean =$3.39
Standard deviation = 0.07
Applying the 2nd rule
2) At least 75% or 3/4 of the data for a set of numbers lies within 2 standard deviations of the mean. The number could be greater.μ - 2σ and μ + 2σ.
the mean =$3.39
Standard deviation = 0.07
μ - 2σ and μ + 2σ.
$3.39 - 2 × 0.07 = $3.25
$3.39 + 2× 0.07 = $3.53
Applying the third rule
3) At least 88.89% or 8/9 of a data set lies within 3 standard deviations of the mean.μ - 3σ and μ + 3σ.
$3.39 - 3 × 0.07 = $3.18
$3.39 + 3 × 0.07 = $3.6
Applying the 4th rule
4) At least 93.75% of a data set lies within 4 standard deviations of the mean.μ - 4σ and μ + 4σ.
$3.39 - 4 × 0.07 = $3.11
$3.39 + 4 × 0.07 = $3.67
Therefore, from the above calculation we can see that the minimum percentage of gasoline stations that had prices between $3.11 and $3.67 corresponds to at least 93.75% of a data set because it lies within 4 standard deviations of the mean.
What would be the answer to number nine
Answer:
x=9.06
Step-by-step explanation:
We have the hypotenuse and we want the opposite of angle a.
so we do
sin65 = x/10.
Solve for x by simplifying both sides of the equation, then isolating the variable.
10. According to a survey, about 58% of families sit down for a fumily dinner at least four times per week. You ask 5 randomly chosen families whether they have a family dinner at least four times per week.
a. Draw a histogram of the binomial distribution for the survey.
b. What is the most likely outcome of the survey?
c. What is the probability that at least 3 families have a family dinner four times per week?
Step-by-step explanation:
Use binomial probability:
P = nCr pʳ qⁿ⁻ʳ
where n is the number of trials,
r is the number of successes,
p is the probability of success,
and q is the probability of failure (1−p).
Given n = 5, p = 0.58, and q = 0.42.
P(0) = ₅C₀ (0.58)⁰ (0.42)⁵⁻⁰ = 0.013
P(1) = ₅C₁ (0.58)¹ (0.42)⁵⁻¹ = 0.090
P(2) = ₅C₂ (0.58)² (0.42)⁵⁻² = 0.249
P(3) = ₅C₃ (0.58)³ (0.42)⁵⁻³ = 0.344
P(4) = ₅C₄ (0.58)⁴ (0.42)⁵⁻⁴ = 0.238
P(5) = ₅C₅ (0.58)⁵ (0.42)⁵⁻⁵ = 0.066
The most likely result is 3 families.
The probability of at least 3 families is:
0.344 + 0.238 + 0.066 = 0.648
Is it geometric or arithmetic? Why
Answer: It is Geometric.
Step-by-step explanation: Because it does not have a fixed pattern that adds or subtract which arithmetic does.
Find the area of the triangle. 13 m 16 m
Answer:
Area = 104
Step-by-step explanation:
The equation to find the area of a triangle is A = 1/2 BH
so if we plug in to numbers into the equation we get
A = 1/2 13*16 no we can multi plier 13*16 and we get 208
and last we can multiply 1/2 to 208 and our final answer is 104
High Hopes^^
Barry-
Please help and please pick between a b c or d
y=5/3x -15 in general form
Answer: 5x - 3y = 45
Step-by-step explanation:
Hope this helps
35% of what is 28?............
35% of 80 is 28.
Answer is 80.
Every day the Washington pet store uses 3/4 of a bag of dog food to feed the dogs his many days will 1 1/2 bags of dog food last
Answer:
2 days
Step-by-step explanation:
Kathy's car runs almost 21 miles on a gallon of gas. If Kathy needs to travel 250
miles, at least how much gas does she need to reach her destination? Express your
answer to the nearest whole gallon.
Оа
Ob
Oc
Od
at least 8 gallons.
at least 10 gallons.
at least 12 gallons.
at least 14 gallons
Answer:
at least 8 gallons
Step-by-step explanation:
Six less than four times a number is 24
written out in numbers
Answer:
4x - 6 = 24
+ 6. +6
4x=30
x=7.5
There are 11 apples in a basket. 5 of these apples are green.the rest of them are red. What are the ratio of all apples to red apples? What is the ratio of green apples to red apples?
Answer:
11/6 or 1 5/6
Step-by-step explanation:
11 = 5 = 6
11/6
simplified it is
1 5/6
Determine the mean, median, mode, and midrange for this collection of class test scores: 88 82 97 76 79 92 65 84 79 90 75 82 78 77 93 88 95 73 69 89 93 78 60 95 88 72 80 94 88 74 a. Mean is 84, median is 82, mode is 82, midrange is 77 b. Mean is 82, median is 88, mode is 88, midrange is 77 c. Mean is 82.4, median is 88, mode is 82, midrange is 78.5 d. Mean is 82.4, median is 82, mode is 88, midrange is 78.5
Mean of a given set of data = Sum of all observations ÷ Total number of observations
Mean of this data set = 88 + 82 + 97 + 76 + 79 + 92 + 65 + 84 + 79 + 90 + 75 + 82 + 78 + 77 + 93 + 88 + 95 + 73 + 69 89 + 93 + 78 + 60 + 95 + 88 + 72 + 80 + 94 + 88 + 74
Mean = 2729 ÷ 30
Mean = 82.4Median = the middle observation in a given set of data
Median of these test scores = 60 , 65 , 69 , 72 , 73 , 74 , 75 , 76 , 77 , 78 , 78 , 79 , 79 , 80 , 82 , 82 , 84 , 88 , 88 , 88 , 88 , 89 , 90 , 92 , 93 , 93 , 94 , 95 , 95 , 97 .
Median = 82 + 82 / 2
= 164 ÷ 2
= 82
Median = 82Mode = most frequently occurring number in a given set of data .
Mode of these test scores =
= 60 = 1 time
= 65 = 1 time
= 69 = 1 time
= 72 = 1 time
= 73 = 1 time
= 74 = 1 time
= 75 = 1 time
= 76 = 1 time
= 77 = 1 time
= 78 = 2 times
= 79 = 2 times
= 80 = 1 time
= 82 = 2 times
= 84 = 1 time
= 88 = 4 times
= 89 = 1 time
= 90 = 1 time
= 92 = 1 time
= 93 = 2 times
= 94 = 1 time
= 95 = 2 times
= 97 = 1 time
Mode = 88Midrange = average of the largest and smallest number in a given set of data
Midrange of these test scores = 97 + 60 / 2
= 97 + 60 / 2
= 157 ÷ 2
= 78.5
Midrange = 78.5Therefore , the correct option is :-
(d) Mean is 82.4 , median is 82 , mode is 88 , midrange is 78.5
What came first into your mind when you read the word “union"? How did you
get the union between the two given sets?
Answer:
well when you hear "union" you think 'joined' or 'together' since thats what it means, In a mathmatical set of numbers, union means that both of the sets are necessary for the equation to be true. I'm not sure what the sets are in this problem but in order to get "union" from anything, that means that when you checked for your domains, the values that you got had to be part of both the given sets
What is the slope of the line that passes through:
(6,5) and (-1,-4)
Thank You!
Answer:
[tex]m=\frac{9}{7}[/tex]
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Simply plug in the 2 coordinates into the slope formula to find slope m:
[tex]m=\frac{-4-5}{-1-6}[/tex]
[tex]m=\frac{-9}{-7}[/tex]
[tex]m=\frac{9}{7}[/tex]
(3x²+5x)-(2x²-3x) simplify
2) Why is it that when you fill the venn diagram with the number of elements, you
always need to start from the intersection of all sets?
Answer:
This is because it is easier this way.
You avoid the problem of putting an element in one set and then realizing that the element also belongs to another set, then you must erase something in order to put the element in both sets. Starting with the intersection allows you to know where will be each set in the diagram, and in this way, the diagram should end up being more readable or "clean".
This may seem small, but being "clean" when doing math, will allow you to have an easier time dealing with a lot of problems. And also will be easier for other people when reading your equations and such.
5,395
- 2,697
How do you solve?
Answer:
2698
Step-by-step explanation:First you take 1000 from 5000 and then distribute it to 395
Answer:
you would subtract 2697 from 5395. you have it in the correct format. the answer would be 2,698.
Step-by-step explanation:
Nicole invested $400 in a fund for 6 years and was paid simple interest. The total interest that she received on the investment was $72. As a
percentage, what was the annual interest rate of her investment?
Answer:
83.3333%
Step-by-step explanation:
The accrued amount of an investment is the original principal P plus the accumulated simple interest, I = Prt, therefore we have:
A = P + I = P + (Prt), and finally A = P(1 + rt)
Complete the multiplication problem to find the answer.
26.1
X3.4
1044
7830
A. 88.74
B. 8874
C. 887.4
D. 87.84
Plzz help
Answer: 88.74
Step-by-step explanation:
Answer:
Answer is 887.4
Step-by-step explanation:
find the value ofx in the equation 3x+1=×+9.
Answer:
x = 4
Step-by-step explanation:
First, you subtract 1 from both sides, giving you 3x = x + 8
Then you subtract 1x from both sides, so 2x = 8
Divide the 2 from both sides which leaves you with the answer, x = 4
An orthocenter of a triangle is
Answer:
the intersection of the triangle's three altitudes.
Step-by-step explanation:
hope this helped </3
How do I solve this?
Answer:
<B = <ABC = 107°
Step-by-step explanation:
<CAB = 32° (property of isosceles triangle)
<ACB = 41° (property of isosceles triangle)
<ABC = ?
<ABC + <ACB + < CAB = 180° (sum of angles of triangle)
<ABC + 41° + 32° = 180°
<ABC + 73° = 180°
<ABC = 180° - 73°
<ABC = 107°
15 points PLEASE HELP
Kirk earns $27.50 an hour and he worked 80 hours this pay period. His deductions are $396 for taxes. $264 for insurance, and $175 for retirement What is
his net pay for this pay period?
Answer:
27.50(80) is 2,200
2,200-396-175-264= 1,365
I think this is how u do it correct me if I'm wrong
Which of the following statements is true?
The number 0 is a natural number.
The number is an integer.
The value π is a rational number.
The number -5 is a real number.
Answer:
The number -5 is a real number is true.
Answer:
what number is the second sentence
A scuba diver dives until he is 45 ft below sea level. His friend is at -12 ft. How many feet are they away from each other?
Answer:
33
Step-by-step explanation:
45 - (-12) = 33
His friend is 33ft away from him.
What is the answer to 6.59+(-7.8)-(2.41)=
This is my question?
(-8.811)(16.29)
I hope you can solve this!!
Answer:
-143.53119
Step-by-step explanation: i think sorry if its wrong
Which one is greater 8 or -12
Answer:
8
Step-by-step explanation:
-12 is below 0 and 8 is above
Answer:
8 is greater
Step-by-step explanation:
the negative sign= - is meaning below so
12 below is -12 which is less so 8 is greater
help please (see below)
Answer:
The quotient is 10x + 16
The remainder is [tex]28x^2 + 10x +22[/tex]
HELP PLEASE !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
65mph
Step-by-step explanation:
Add 100 and 30 together then divide by 2. You get 65 miles per hour.