Historically,a company that mails its monthly catalog to potential customers receives 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 received from this sample?
A) 0.0496
B) 0.2049
C) 0.7444
D) 0.7951
E) 0.9504

Question

Quizplus · Accepted Answer

This problem can be solved using the binomial distribution formula:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
where
X = number of orders received from the sample
n = size of the sample (500)
k = number of orders received (between 35 and 50)
p = probability of getting an order from a single address (0.08)

We need to find the probability of getting between 35 and 50 orders, so we need to calculate the sum of probabilities for all values of k between 35 and 50:
P(35<=X<=50) = P(X=35) + P(X=36) + ... + P(X=50)

Using a calculator or a spreadsheet, we can calculate this probability to be approximately 0.7444.

Therefore, the best choice is C, which corresponds to this answer.

Historically,a Company That Mails Its Monthly Catalog to Potential Customers