In: Statistics and Probability
The following information has been provided about the population mean (μ) and population standard deviation (σ):
μ=2365, σ=340
We need to compute:
Pr(1685≤X≤3045)
Notice that in this case, we have that:
= 2
Since these two values coincide, it means that the event (1685, 3045) is centered around the mean μ=2365 and, also, the event 1685≤X≤3045) is equivalent to having X to be within 2 standard deviations of the mean
According to Chebyshev's rule, the probability that XX is within kk standard deviations of the mean is estimated as shown below:
In this case, since k = 2 the probability that X is within 2 standard deviations of the mean is at least:
=Pr(1685≤X≤3045)≥1−221=0.75
Interpretation: The above results does not tell you that the probability that X is within 2 standard deviations of the mean is at equal to 0.75.
the percentage of homeowners in this town who pay between $1685 and $3045. is 0.75