1. Typing errors per page for a certain typing pool are known to follow this

probability distribution:

x P(x)

0 0.01

1 0.09

2 0.30

3 0.20

4 0.20

5 0.10

6 0.10

1. Verify that P(x) is a probability distribution.
2. Find the cumulative distribution function.
3. Find the probability that at most four errors will be made on a page.
4. Find the probability that at least two errors will be made on a page.

1. An automobile dealership records the number of cars sold each day. The data are used in calculating the following probability distribution of daily sales:
   x P(x)
   0 0.1
   1 0.1
   2 0.2
   3 0.2
   4 0.3
   5 0.1
   1. Find the probability that the number of cars sold tomorrow will be between two and four (both inclusive).
   2. Find the cumulative distribution function of the number of cars sold per day.
   3. Show that P(x) is a probability distribution.

Suppose the car dealership’s operation costs are well approximated by the square root of the number of cars sold, multiplied by $300. What is the expected daily cost of the operation? Explain.

1. A large shipment of computer chips is known to contain 10% defective chips. If 100 chips are randomly selected, what is the expected number of defective ones? What is the standard deviation of the number of defective chips? Use Chebyshev’s theorem to give bounds such that there is at least a 0.75 chance that the number of defective chips will be within the two bounds.

1. A random variable X is described in each of the following items. Find out which standard distribution X is likely to follow in each case.

1. X is the number of rescue calls received at a 911 call center on a given day.
2. Your friend is equally likely to be found at any one of a number of places during coffee break. X is the number of places you have to look to find him.
3. A drawer contains 8 red socks and 12 green socks. You pick 6 socks at random from the drawer. X is the number of red socks you picked.
4. An assembly line breaks down and stops about once in six months. X is the number of times it breaks down in a given year.
5. X is the time gap between two successive crashes of a mainframe computer.
6. A company buys bolts in bulk and rarely finds defective ones. X is the number of defective bolts in the shipment that just arrived.
7. Twenty students take a test in which each of them has a 30% chance of getting an A grade. X is the number of students who get A grades.
8. You need six volunteers for a task and you ask your friends one by one until you get six volunteers. Each friend has a 60% chance of agreeing to volunteer. X is the number of friends you have to ask.
9. Fifty guests are sent invitations to a party, and each guest has an 80% chance of attending the party. X is the number of guests who actually show up.
10. A factory has a large number of machines that occasionally break down. X is the number of machines that break down on a given day.
11. A machine breaks down occasionally. X is the time gap between two successive breakdowns.
12. Headline News on TV starts every half hour. You switch on the TV at a random time and wait till the start. X is the time you have to wait.
13. A committee is formed by picking members at random from the U.S. Senate. X is the number of democrats picked.
14. An airline has sold 132 tickets for a flight. Each ticket buyer has a 96% chance of showing up. X is the actual number of passengers who show up.
15. A company sends out tens of thousands of free samples to prospective customers, each of whom has a very small chance of buying the product. X is the actual number of customers who buy the product.
16. A machine breaks down occasionally. You visit the machine and wait till it breaks down. X is the time you have to wait.
17. A shuttle bus leaves an airport every 45 minutes. You arrive at a random time and wait for it. X is the time you have to wait.

1. A mainframe computer in a university crashes on the average 0.71 times in a semester.

1. What is the probability that it will crash at least two times in a given semester?
2. What is the probability it will not crash at all in a given semester?
3. The MIS administrator wants to increase the probability of no crashes at all in a semester to at least 90%. What is the largest µ that will achieve this goal?

1. Laptop computers produced by a company have an average life of 38.36 months. Assume that the life of a computer is exponentially distributed (which is a good assumption).

1. What is the probability that a computer will fail within twelve months?
2. If the company gives a warranty period of 12 months, what proportion of computers will fail within the warranty period?
3. Based on the answer to (b), would you say that the company can afford to give a warranty period of 12 months?
4. If the company wants not more than 5% of the computers to fail during the warranty period, what should be the warranty period?
5. If the company wants to give a warranty period of three months and still wants not more than 5% of the computers to fail during the warranty period, what should be the minimum average life of the computers?

Price: $27.95

Solution: The downloadable solution consists of 11 pages, 1695 words and 62 charts.
Deliverable: Word Document