26. Your customers\' average order size is $2,601, with a standard deviation of

Question

26. 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 indepen- dently 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 indi- vidual customer orders are somewhat skewed? d.* Find the probability that total orders will be at or e.) Find the probability of a truly amazing day, with f. Find the probability of a typical day, with total orders 8 Find the probability of a surprising day, with total h. What are the chances that tomorrow's average above your break-even point of $105,000. total orders exceeding $135,000. between $110,000 and $125,000. orders either below $100,000 or above $135,000. order per customer will be between $2,450 and $2,750? L.

Explanation / Answer

mean order size per customer = 2601
std. dev. per customer = 1275

For 45 customers
mean = 2601 * 45 = 117045
std. dev. = 1275*sqrt(45) = 8552.96

e)
P(X>135000)
= P(z > (135000 - 117045)/8552.96)
= P(z > 2.0993)
= 0.0179 (use standard z-table)

f)
P(110000 < X < 125000)
= P((110000 - 117045)/8552.96 < z < (125000 - 117045)/8552.96)
= P(-0.8237 < z < 0.9301)
= P(z < 0.9301) - P(z < -0.8237)
= 0.8238 - 0.2051 (use standard z-table)
= 0.6188

g)
P(X<100000)
= P(z < (100000 - 117045)/8552.96)
= P(z < -1.9929)
= 0.0231 (use standard z-table)

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