While attending a trade convention, you find a note abandoned by one of your keenest competitors. On it, she has written the mean and standard deviation of her population of sales orders: "mean = $100, standard deviation = $30". You are convinced these values are genuine. But you are a little surprised, for your mean ($110) is higher than hers, and your standard deviation ($20) is lower. You thought she would have a higher average sales order and also have less variable sales. Armed with this information, you decide to do some speculative, but reasonable calculations. The note does not say what the shape of her distribution is, but you are willing to assume that it is normal, since your sales distribution is normal.

1. Based on your experience, you know that orders less than $70 are net losers. You are willing to assume that your competitor's cost structure is similar to yours. What proportion of her orders are net losers?

2. What proportion of your orders are net losers (less than $70)?

3.Again, based on your experience, you know that the greatest profit is made on the high-dollar orders - those orders that are over $150. What proportion of your competitor's orders is in the high-dollar category?

4. What proportion of your orders is in the high-dollar category (over $150)?

5. If you decide to offer free shipping to the top 10% of your orders, what size order qualifies?

6. If your competitor matches you with free shipping for the top 10% of her orders, what size order qualifies for her?