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?