Question: Your customers' average order size is $2,601, with a standard deviation of $1,275. You are wondering what would happen if exactly 45 typical customers independently placed orders tomorrow.
a. Find the mean of tomorrow's total orders.
b. Find the standard deviation of tomorrow's total orders.
c. Next (for the rest of this problem) assume that tomorrow's total orders follow a normal distribution. Why is this assumption reasonable, even if individual customer orders are somewhat skewed?
d. Find the probability that total orders will be at or above your break-even point of $105,000.
e. Find the probability of a truly amazing day, with total orders exceeding $135,000.
f. Find the probability of a typical day, with total orders between $110,000 and $125,000.
g. Find the probability of a surprising day, with total orders either below $100,000 or above $135,000.
h. What are the chances that tomorrow's average order per customer will be between $2,450 and $2,750?