Solve: (2a^2+5a+2)^1/2=3 a = -7/2 a = 1 a = -7/2 or a = 1 no real solution
2 answers:
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Answer:
(a) The percentage of gasoline stations had prices within 4 standard deviations of the mean is 93.75%.
(b) The percentage of gasoline stations had prices within 1.5 standard deviations of the mean is 55.56%. The prices for this stations goes from $3.325 to $3.535.
(c) The minimum percentage of stations that had prices between $3.22 and $3.64 is 88.88%.
Step-by-step explanation:
The Chebyshev's inequality states that at least 1-(1/K^2) of data from a sample must fall within K standard deviations from the mean, being K any positive real number greater than one.
It can be expressed as
In this problem, we have, for the gasoline price, a normal distribution with mean of 3.43 and standar deviation of 0.07.
(a) The percentage of gasoline stations had prices within 4 standard deviations of the mean is equal to <em>one less the percentage of gasoline stations that had prices out of 4 standard deviations of the mean:</em>
The percentage of gasoline stations had prices within 4 standard deviations of the mean is 93.75%.
(b) The percentage of gasoline stations had prices within 1.5 standard deviations of the mean is 55.56%.
The prices for this stations goes from $3.325 to $3.535.
(c) To answer, we have to calculate k for this range of prices:
For k=3, the Chebyshev's inequality states:
So, the minimum percentage of stations that had prices between $3.22 and $3.64 is 88.88%.