1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Anvisha [2.4K]
3 years ago
9

At one point the average price of regular unleaded gasoline was ​$3.39 per gallon. Assume that the standard deviation price per

gallon is ​$ per gallon and use​ Chebyshev's inequality to answer the following. ​(a) What percentage of gasoline stations had prices within standard deviations of the​ mean? ​(b) What percentage of gasoline stations had prices within standard deviations of the​ mean? What are the gasoline prices that are within standard deviations of the​ mean? ​(c) What is the minimum percentage of gasoline stations that had prices between ​$ and ​$​?
Mathematics
1 answer:
irinina [24]3 years ago
4 0

This question was not written completely

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.

You might be interested in
A can of soup has a diameter of 2.5 inches and a height of 4 inches. What is the area of the label for the can? Round your answe
il63 [147K]

Answer:

Step-by-step explanation:

Diameter d = 2.5 inches

Height h = 4 inches

Lateral area = πdh =π(2.5)(4) = 10π ≈ 31.4 square inches

4 0
3 years ago
A company that sells phones generates revenue given by the function
Anon25 [30]
Profit = Revenue - Cost = R(x) - C(x) = (x^2 + 20x + 50) - (50x + 30) = x^2 - 30x + 20
8 0
2 years ago
Find the sum of the interior angles of a regular 29-gon.
Oliga [24]
The answer is (n-2)180
7 0
3 years ago
Read 2 more answers
The ratio of a model building's dimensions to the building's actual dimensions is 1/52. If the height of the model is 15 inches,
g100num [7]
Set this up as a proportion with the model stuff on top and actual building stuff on bottom.  \frac{1}{52} = \frac{15}{x}.  Cross multiply to get x = 780.  The actual building is 780 inches.  In feet that is 65.
4 0
3 years ago
4) 16 + 7 + 9 = 7 + 9 + 16 *
nlexa [21]

Answer:

a.) Commutative Property of addition

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Other questions:
  • Brody and Amanda can you for one hour and 20 minutes before serving to fish at 1:50 PM at what time did they start canoeing
    13·2 answers
  • Least to greatest 0.44,3/8,0.5,2/5
    15·2 answers
  • Please help!!!<br> Due Monday (tomorrow)
    10·1 answer
  • What is the volume of one cylinder?
    6·2 answers
  • A science class has
    13·1 answer
  • Please help if you can!
    10·2 answers
  • Please help with this question!!
    6·2 answers
  • A system of equations is shown below:
    9·1 answer
  • If there are 10 apples in the fridge and 7 on the table, what is the ratio of apples in the fridge to all the apples?
    6·1 answer
  • Please help this question​
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!