The mean monthly mortage payment for homwowners in the local community was $2365, and the standard...

The mean monthly mortage payment for homwowners in the local community was $2365, and the standard deviation was $340. Using Chebyshev’s therorem, calculate the percentage of homeowners in this town who pay between $1685 and $3045.

Solutions

Expert Solution

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

orchestra answered 11 months ago

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