Chebyshev's thereon- the author's generac produces voltage amounts with a mean of 125.0 volts and a standard deviation of 0.3 volt. using chebyshev's theorem,what do we know about the percentage of voltage amounts that are within 3 standard deviations of the mean? What are the minimum and maximum voltage amounts that are within 3 standard deviations of the mean?
Within 3SD on either side are .4987. Multiply by 200 to get percentage.
You want mean ± 3 SD for min and max. Insert the values and solve.
To use Chebyshev's theorem to determine what we know about the percentage of voltage amounts within 3 standard deviations of the mean, we can use the following formula:
Percentage within k standard deviations (P) = 1 - (1/k^2)
In this case, k is 3 (since we want to find out the percentage within 3 standard deviations). Plugging in the value of k into the formula, we get:
P = 1 - (1/3^2)
P = 1 - (1/9)
P = 8/9
So, we know that at least 8/9 (or approximately 88.89%) of the voltage amounts lie within 3 standard deviations of the mean.
Now, to find the minimum and maximum voltage amounts within 3 standard deviations of the mean, we can use the following formulas:
Minimum value = Mean - (k * standard deviation)
Maximum value = Mean + (k * standard deviation)
Plugging in the values we have:
Minimum value = 125.0 - (3 * 0.3)
Minimum value = 125.0 - 0.9
Minimum value = 124.1 volts
Maximum value = 125.0 + (3 * 0.3)
Maximum value = 125.0 + 0.9
Maximum value = 125.9 volts
Therefore, the minimum voltage amount within 3 standard deviations of the mean is 124.1 volts, and the maximum voltage amount is 125.9 volts.