Statistics and Probability Sample Problems

1. In a recent study 90 percent of the homes in the United States were found to have color TVs. In a sample of nine homes, what is the probability that:
a. All nine have color TVs?
b. Less than five have color TVs?
c. More than five have color TVs?
d. At least seven homes have color TVs?

2. Thirty percent of the population in a southwestern community are Spanish-speaking Americans. A Spanish-speaking person is accused of killing a non-Spanish-speaking American. Of the first 12 potential jurors, only 2 are Spanish-speaking Americans, and 10 are not. The defendant's lawyer challenges the jury selection, claiming bias against her client. The government lawyer disagrees, saying that the probability of this particular jury composition is common. What do you think?

3. The Director of Emergency Medicine at Big Mountain Medical Services is studying patient waiting time. Waiting time is defined as the time from when a patient enters the facility until seen by a physician. The study indicates the waiting time follows a normal distribution with a mean of 22 minutes and a standard deviation of 8 minutes.
a. What fraction of the patients is seen in between 15 and 22 minutes?
b. What fraction is seen in less than 15 minutes?
c. What fraction is seen in more than 15 minutes but less than 32 minutes?
d. What fraction is seen in more than 25 minutes but less than 32 minutes?
e. Five percent of the patients are seen in how many minutes or less? That is, how quickly are 5
percent of the patients seen?

4. A study of Furniture Wholesales, Inc. 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 Furniture Wholesales 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 working days of the receipt of the invoice. What percent of customers will earn this discount?