# probabilities

• Feb 6th 2009, 02:27 PM
jax760
probabilities
Historically, a company that mails it's monthly catalog to potential customers recieves orders from 8 percent of the addresses. If 500 addresses are selected randomly from the last mailing, what is the probability that between 35 and 50 orders were recieved from this sample?
• Feb 6th 2009, 06:03 PM
Rapha
Hello.

Quote:

Originally Posted by jax760
Historically, a company that mails it's monthly catalog to potential customers recieves orders from 8 percent of the addresses. If 500 addresses are selected randomly from the last mailing, what is the probability that between 35 and 50 orders were recieved from this sample?

So you ask about two different probabilities. first: exact 35 orders; second: exact 50 orders

the probability "exact 35 orders" is according to the binomial distribution

$\displaystyle \begin{pmatrix} 500 \\ 35 \end{pmatrix}0.08^{35} * 0.92^{500-35}$

p(exact 50 orders) = $\displaystyle \begin{pmatrix} 500 \\ 50 \end{pmatrix}0.08^{50} * 0.92^{500-50}$

Edit:
OH yea, actually it is "between 35 and 50". I didn't read the word "between". That makes a big difference. Thanks to mr fantastic

In that case you have to sum the probabilities like this

$\displaystyle \begin{pmatrix} 500 \\ 35 \end{pmatrix}0.08^{35} * 0.92^{500-35}+\begin{pmatrix} 500 \\ 36 \end{pmatrix}0.08^{36} * 0.92^{500-36}+...+\begin{pmatrix} 500 \\ 50 \end{pmatrix}0.08^{50} * 0.92^{500-50}$

Sorry for the mistake.

Regards
Rapha
• Feb 6th 2009, 08:22 PM
mr fantastic
Quote:

Originally Posted by jax760
Historically, a company that mails it's monthly catalog to potential customers recieves orders from 8 percent of the addresses. If 500 addresses are selected randomly from the last mailing, what is the probability that between 35 and 50 orders were recieved from this sample?

Quote:

Originally Posted by Rapha
Hello.

So you ask about two different probabilities. first: exact 35 orders; second: exact 50 orders

the probability "exact 35 orders" is according to the binomial distribution

$\displaystyle \begin{pmatrix} 500 \\ 35 \end{pmatrix}0.08^{35} * 0.92^{500-35}$

p(exact 50 orders) = $\displaystyle \begin{pmatrix} 500 \\ 50 \end{pmatrix}0.08^{50} * 0.92^{500-50}$

Regards
Rapha

Actually the cumulative probability $\displaystyle \Pr(35 \leq X \leq 50)$ is required where X ~ Binomial(n = 500, p = 0.08).