How Do Sales Representatives' Earnings Vary in a Canadian Clothing Chain?

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SUMMARY

The discussion focuses on the earnings variability of sales representatives in a Canadian clothing chain with offices in Toronto, Montreal, Vancouver, and Calgary. The weekly sales figures are normally distributed, with a mean of $12,000 and a standard deviation of $2,000. The probability of a representative's weekly sales falling within a specific range around the mean is 0.9973, which corresponds to approximately ±3 standard deviations from the mean. This implies that individual sales will typically range from $6,000 to $18,000, while the average sales for the Montreal office and the entire company will also fall within this range.

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This discussion is beneficial for sales analysts, statisticians, and business managers interested in understanding sales performance metrics and variability within retail environments.

adeel
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A clothing store has offices in Toronto, Montreal, Vancouver and Calgary, and each office has 25 sales representatives. The weekly sales for the sales representatives are normally distributed with a mean of $12,000 and a standard deviation of $ 2,000. Within what range about the mean is the probability 0.9973 that:

1. A given representatives weekly sales will fall
2. The average weekly sales per representative of the Montreal office will fall
3. The average weekly sales per representative of the company will fall.

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I have the answers, but I have no idea from where to even begin. If someone can help me understand and explain this id be very appreciative.
 
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I don't quite understand the wording of (1) or the rest of the question about the range of the mean enough to give a complete answer.

If a representative has sales of x for week one, then the probability of him having less than x sales for the next week is the integral of the normal distribution from -infinity to x.

If you give the answer to (1) maybe one could work backward and understand the wording better.