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
Vikentia [17]
3 years ago
13

At one point the average price of regular unleaded gasoline was ​$3.41 per gallon. Assume that the standard deviation price per

gallon is ​$0.09 per gallon and use​ Chebyshev's inequality to answer the following. ​
(a) What percentage of gasoline stations had prices within 2 standard deviations of the​ mean?
​(b) What percentage of gasoline stations had prices within 1.5 standard deviations of the​ mean? What are the gasoline prices that are within 1.5 standard deviations of the​ mean? ​
(c) What is the minimum percentage of gasoline stations that had prices between ​$3.05 and ​$3.77​?
Mathematics
1 answer:
Aleonysh [2.5K]3 years ago
3 0

Answer:

a)  1-\frac{1}{k^2} =1- \frac{1}{2^2}= 1-0.25 = 0.75

So we expected about 75% within two deviations from the mean

b) 1-\frac{1}{k^2} =1- \frac{1}{1.5^2}= 1-0.4444 = 0.556

So we expected about 55.6% within 1.5 deviations from the mean

And the limits are:

Lower = 3.41 -1.5*0.09 = 3.275

Upper = 3.41 +1.5*0.09 = 3.545

c) We can calculate how many deviations we are within the mean with the limits with this formula:

z =\frac{x-\mu}{\sigma}

And using the lower limit we got:

z = \frac{3.05-3.41}{0.09}=-4

And with the upper limit we got:

z = \frac{3.77-3.41}{0.09}=4

So then the value of k =4 and the percentage is given by:

1-\frac{1}{k^2} =1- \frac{1}{4^2}= 1-0.0625 = 0.9375

Step-by-step explanation:

Previous concepts and Data given  

\mu =3.41 reprsent the population mean

\sigma=0.09 represent the population standard deviation

The Chebyshev's Theorem states that for any dataset

• We have at least 75% of all the data within two deviations from the mean.

• We have at least 88.9% of all the data within three deviations from the mean.

• We have at least 93.8% of all the data within four deviations from the mean.

Or in general words "For any set of data (either population or sample) and for any constant k greater than 1, the proportion of the data that must lie within k standard deviations on either side of the mean is at least: 1-\frac{1}{k^2}

Part a

For this case we can find the percentage required replaincg k =2 and we got:

1-\frac{1}{k^2} =1- \frac{1}{2^2}= 1-0.25 = 0.75

So we expected about 75% within two deviations from the mean

Part b

For this case we can find the percentage required replaincg k =2 and we got:

1-\frac{1}{k^2} =1- \frac{1}{1.5^2}= 1-0.4444 = 0.556

So we expected about 55.6% within 1.5 deviations from the mean

And the limits are:

Lower = 3.41 -1.5*0.09 = 3.275

Upper = 3.41 +1.5*0.09 = 3.545

Part c

We can calculate how many deviations we are within the mean with the limits with this formula:

z =\frac{x-\mu}{\sigma}

And using the lower limit we got:

z = \frac{3.05-3.41}{0.09}=-4

And with the upper limit we got:

z = \frac{3.77-3.41}{0.09}=4

So then the value of k =4 and the percentage is given by:

1-\frac{1}{k^2} =1- \frac{1}{4^2}= 1-0.0625 = 0.9375

You might be interested in
Since nobody answered my other questions, can someone please show me how to solve and answer 14 and 15 all the parts? Please I n
ozzi
Sure : Do 3,000 x 6 and you will see what you get and that’s the answer
3 0
3 years ago
Enter the solution (x,y) to the system of equations shown.<br> y= -6<br> y= 4x+12
andriy [413]
Y= -6 --> plug this -6 into the y of the 2nd equation
y= 4x+12 --> -6 = 4x+12 --> 4x = -18
x = -18/4 = -9/2 --> now this is the x solution coordinate, and we know that y must equal -6 from the 1st equation, so our solution point is:
(-9/2, -6)
Hope that helped!
6 0
3 years ago
Read 2 more answers
There are 850 employees at a software company. The company’s CEO was interested in finding out if his employees prefer the new c
mixas84 [53]

Answer: B & E

i just took it

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Changing 25/4 fraction into a mixed fraction
Veronika [31]
Divide 25 by 4 and you get 6 with a remainder of 1. That remainder of 1 can go over 4 to create the final answer of 6 and 1/4. 
6 0
3 years ago
Read 2 more answers
Write the equation of the circle with center (0,0) and (3,6)
ruslelena [56]
Ya I cant help you :/
7 0
3 years ago
Other questions:
  • your friend says that the absolute value equation | 3x + 8 |-9= -5 has no solution because the constant on the right side of the
    8·1 answer
  • What is x divided by -6
    13·1 answer
  • HELP ME PLZ!!!! A bakery sold 48 chocolate cupcakes in a day, which was 12% of the total number of cupcakes sold that day. How m
    6·1 answer
  • Please do all of the attachments, quick. It is due please
    13·1 answer
  • (-16, -4) (0,-12) slope
    9·2 answers
  • May I know this answer
    8·1 answer
  • Sara wants to buy a tennis racket for $120. She has $40 and is saving $10 every week. The owner of the store decreases the racke
    15·1 answer
  • Are these triangles congruent ?
    7·2 answers
  • I’ll give brainliest, thanks and 5 stars.
    5·1 answer
  • Write an equation for converting the number of meters to kilometers
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!