Answer: mean monthly income = $5000
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Explanation
In any normal distribution, the median and mean are the same value.
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The proof is as follows:
If mean > median was the case, then the distribution would be skewed to the right (ie positively skewed). The right tail is pulled longer than the left tail. But this would contradict the symmetrical nature of the normal distribution. So mean > median must not be the case.
If mean < median, then the distribution would be skewed to the left (negatively skewed). Visually this pulls the left tail longer than the right tail. Like in the previous paragraph, this contradicts the symmetrical nature of the normal distribution. So mean < median must not be the case.
Since mean > median cannot be true, and neither can mean < median, this must indicate mean = median.
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So in short, any symmetrical distribution always has mean = median and they are at the very center of the distribution.
