Suppose that mean retail price per gallon of regular grade gasoline is $3.45 with a standard deviation of $0.10 and that the retail
price per gallon has a bell-shaped distribution.
NOTE: Please use empirical rule approximations for this problem.
a. What percentage of regular grade gasoline sells for between $3.35 and $3.55 per gallon (to 1 decimal)?
Lololo
%
b. What percentage of regular grade gasoline sells for between $3.35 and $3.65 per gallon (to 1 decimal)?
%
c. What percentage of regular grade gasoline sells for less than $3.55 per gallon (to 1 decimal)?
%
Answers
The percentage of regular grade gasoline sells for between $3.35 and $3.55 per gallon is 64%
The percentage of regular grade gasoline sells for between $3.35 and $3.65 per gallon is 81.5%
The percentage of regular grade gasoline sells for less than $3.55 per gallon is 84%
Given :
Mean retail price is $3.45
Standard deviation is 0.10
Empirical rule states that 99.7% of data is observed in normal distribution that lies within 3 standard deviations.
68% of data lies under 1 standard deviation
95% lies under 2 standard deviations
99.7% lies under 3 standard deviations
there are 3 standard deviations on the left and right of mean . The graph is attached below
Mean is 3.45. standard deviation is 0.1
3.45+0.1=3.55
3.45-0.1=3.35
So 3.35 and 3.55 lies under first standard deviation
The percentage between $3.35 and $3.55 is 68%
3.45 +0.1+0.1=3.65
3.35 lies on 1 standard deviation on left and 2 deviations on the right of mean
So , 34+34+13.5=81.5%
The percentage between $3.35 and $3.65 is 81.5%
For gasoline sells for less than 3.55 , there are 3 standard deviation on the left of mean and 1 standard deviation on the right
0.15+2.35+13.5+34+34=84%
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