Score: 0 of 1 pt 5 of 5 (4 complete) HW Score: 70.48%, 3.52 of 5 pts 3.2.35 Ques
ID: 3062693 • Letter: S
Question
Score: 0 of 1 pt 5 of 5 (4 complete) HW Score: 70.48%, 3.52 of 5 pts 3.2.35 Question Help At one point the average price of regular unleaded gasoline was $3.59 per gallon. Assume that the standard deviation price per gallon is S0.09 per gallon and use Chebyshev's inequality to answer the following. (a) What percentage of gasoline stations had prices within 4 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 S3.41 and $3.77? (a) At least (Round to two decimal places as needed.) % of gasoline stations had prices within 4 standard deviations of the mean (b) At least (Round to two decimal places as needed.) % of gasoline stations had prices within 1.5 standard deviations of the mean. The gasoline prices that are within 1.5 standard deviations of the mean are to S (Use ascending orderExplanation / Answer
According to Chebyshev's theorem, at least (11/k2) of the data lie within k standard deviations of the mean, that is, in the interval with endpoints x¯± ks for samples and with endpoints ± k for populations, where k is any positive whole number that is greater than 1.
a)
For k = 4,
(1 - 1/4^2) = 15/16 = 93.75%
At least 93.75% of gasoline stations had prices within 4 standard deviations of the mean.
b)
For k = 1.5,
(1 - 1/1.5^2) = 55.56%
At least 55.56% of gasoline stations had prices within 1.5 standard deviations of the mean.
3.59 - 1.5*0.09 = 3.455
3.59 + 1.5*0.09 = 3.725
The gasoline prices that are within 1.5 sd of the mean are $3.455 to $3.725
c)
Here we need to find the k first
(3.77 - 3.41)/2 = 0.18 = 2*sd
hence k = 2
For k = 2,
(1 - 1/2^2) = 3/4 = 75%
At least 75% of gasoline stations had prices within 2 standard deviations of the mean i.e. between $3.41 and $3.77.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.