Week 5 - Application Assignment - 16 points

In problems below, all probabilities must be calculated using a TI83 or TI84 calculator. Be sure to list the calculator function in its entirety as your work for each problem. List the formulas for the mean and standard deviation as your work for those calculations as appropriate.

1. (8 points)At a college bookstore, 28% of student customers who have to buy a textbook for a course bought a new copy, whereas the remaining 72% preferred a used copy.The bookstore manager selected a random sample of 20 student patrons who purchased a textbook from the bookstore.

Answer the following questions. Include your calculator functions for each probability question and round your answers to 4 digits.

1. (1 pt) What is the probability that exactly 4 students purchased a new textbook?

1. (1 pt) What is the probability that at most 12 students purchased a new textbook?

1. (1 pt) What is the probability that at least 9 students purchased a new textbook?

1. (1 pt) What is the probability that exactly 15 students purchased a used textbook?

1. (1 pt) What is the probability that fewer than 14 students purchased a used textbook?

1. (1 pt) What is the probability that more than 10 students purchased a used textbook?

1. (2 pts) Find the mean and standard deviation of the students who purchased a new textbook. Show your formula setup and your work.

1. (8 points) The following percentages were obtained over many years of observation by the U.S. Weather Bureau. All data listed are for the month of December.

Location	Long-Term Mean % of Clear Days in Dec.
Juneau, Alaska	18%
Seattle, Washington	24%
Hilo, Hawaii	36%
Las Vegas, Nevada	75%
Phoenix, Arizona	77%

In the locations listed, the month of December is a relatively stable month with respect to weather. Since weather patterns in these locations from one day to the next are more or less the same, it is reasonable to use a binomial probability model.

Let r be the number of clear days in December. Since December has 31 days, is the binomial probability for each of the listed locations when . Include your formula setup or calculator functions to answer the following questions.

1. (1 pt) Find the probability that Juneau will have at most 8 clear days in December.

1. (1 pt) Find the probability that Hilo will have at least 14 clear days in December.

1. (1 pt) Find the probability that Phoenix will have 20 or more clear days in December.

1. (1 pt) Find the probability that Las Vegas will have no more than 18 clear days in December.

1. (2 pts) Find the probability that Seattle will have from 5 to 10 (including 5 and 10) clear days in December.

1. (2 pts) Find the mean number of clear days in December in each of these locations. Fill in the table below. Round your answers to two decimal digits.

Location	Mean number of clear days in December
Juneau, Alaska
Seattle, Washington
Hilo, Hawaii
Las Vegas, Nevada
Phoenix, Arizona