The problem asks to determine the expected value of online sales for different types of shoes on launch day.

We are given:

• Number of visitors: 4403 people
• Shoe types, prices, and probabilities:
  • Sneakers: Price = $67.99, Probability = $\frac{3}{25}$
  • High heels: Price = $62.25, Probability = $\frac{1}{20}$
  • Sandals: Price = $43.50, Probability = $\frac{3}{10}$
  • Loafers: Price = $55.75, Probability = $\frac{3}{20}$

To find the expected spending per person, we compute the expected value $E$ using the formula:

$E = (\text{Price of Sneakers} \times P(\text{Sneakers})) + (\text{Price of High Heels} \times P(\text{High Heels})) + (\text{Price of Sandals} \times P(\text{Sandals})) + (\text{Price of Loafers} \times P(\text{Loafers}))$

The total expected amount spent by all visitors will be:

$\text{Total Expected Sales} = E \times 4403$

Let me calculate this now.The expected spending per person on the website is approximately $32.68.

Thus, the company should expect total sales of about $143,906.77 on launch day from 4403 visitors.

Would you like more details or have any questions?

Here are five related questions to expand your understanding:

1. How would the expected sales change if the probabilities for each shoe type were different?
2. What happens to the expected sales if fewer visitors arrive on launch day?
3. How is the expected value formula applied in other real-life business decisions?
4. How can the company adjust marketing to increase the probability of buying higher-priced shoes?
5. What effect would offering discounts on these shoes have on the overall expected sales?

Tip: Expected value is a crucial concept in decision-making and can be applied to assess risk in financial investments, business strategies, or even personal decisions.