# Probability question

1. Jun 8, 2005

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.

2. Jun 8, 2005

### juvenal

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.