1. ## Homework 2

A study of Hub Furniture regarding the payment of invoices reveals the time from billing until payment is received follows the normal distribution. The mean time until payment is received is 20 days and the standard deviation is 5 days.

a. What percent of the invoices are paid within 15 days of receipt?

b. What percent of the invoices are paid in more than 28 days?

c. What percent of the invoices are paid in more than 15 days but less than 28 days?

d. The management of Hub Furniture wants to encourage their customers to pay their monthly invoices as soon as possible. Therefore, it announced that a 2 percent reduction in price would be in effect for customers who pay within 7 days of the receipt of the invoice. What percent of customers will earn this discount?

Hint: After deriving your answer, think about it logically. For example, can the probability that an invoice is paid in more than 28 days be greater than 0.5 when the mean is 20? No, it certainly must be less than 0.5, and probably much less.

If the average number of defects in a Poisson distribution is 3, what is the probability of 2 or more defects?

2. Originally Posted by Aala
A study of Hub Furniture regarding the payment of invoices reveals the time from billing until payment is received follows the normal distribution. The mean time until payment is received is 20 days and the standard deviation is 5 days.

a. What percent of the invoices are paid within 15 days of receipt?

b. What percent of the invoices are paid in more than 28 days?

c. What percent of the invoices are paid in more than 15 days but less than 28 days?

d. The management of Hub Furniture wants to encourage their customers to pay their monthly invoices as soon as possible. Therefore, it announced that a 2 percent reduction in price would be in effect for customers who pay within 7 days of the receipt of the invoice. What percent of customers will earn this discount?

[snip]
Let X be the random variable number of days until payment.

Then X ~ Norm $(\mu = 20\,$, $\sigma = 5)$.

a. 100 Pr(X < 15)

b. 100 Pr(X > 28)

c. 100 Pr(15 X < 28)

d. 100 Pr(X < 7)

In each case the calculation of the probability should be routine.

Originally Posted by Aala
[snip]
If the average number of defects in a Poisson distribution is 3, what is the probability of 2 or more defects?
1. As you should already realise, $\Pr(X = x) = \frac{e^{-3} \, 3^x}{x!}$.

2. $\Pr(X \geq 2) = 1 - \Pr(X \leq 1) = 1 - \Pr(X = 0) - \Pr(X = 1)$.