Please read the additional materials. Ignore the following below. Thank you. BUS 190HW 9 Random variables, binomial, uniform, normal AS USUAL- SHOW YOUR WORK- SHOW GRAPHS WHERE APPROPRIATE General random variable Suppose you have a box of 10 tickets, with 3 green tickets and 7 yellow tickets. If you pick a green ticket out of the box, you get $10. If you pick a yellow ticket, you have to pay $5.Let the random variable X be the amount you get (if you have to pay, it is negative pay) after 1 draw from this box. Set up the table for this random variable X, and indicate why it is a good random variable table (hint: check valid probability for each value of X and they sum to 1).

chapter_3.docx

Unformatted Attachment Preview

Don't use plagiarized sources. Get Your Custom Essay on

binomial uniform and normal

Just from $13/Page

BUS 190

HW 9 Random variables, binomial, uniform, normal

AS USUAL – SHOW YOUR WORK- SHOW GRAPHS WHERE APPROPRIATE

1. General random variable

Suppose you have a box of 10 tickets, with 3 green tickets and 7 yellow tickets. If you pick a green

ticket out of the box, you get $10. If you pick a yellow ticket, you have to pay $5. Let the random

variable X be the amount you get (if you have to pay, it is negative pay) after 1 draw from this box.

a. Set up the table for this random variable X, and indicate why it is a good random variable table

(hint: check valid probability for each value of X and they sum to 1).

b. Calculate E(X)

c. Calculate Var(X)

d.

2. Binomial

Suppose according to past data for a small boutique, about 30% of the customers who walk into

the store purchase at least one item.

a. Today 10 individual customers walked into the store while you are there. How many of these 10

customers do you expect would by at least one item? (hint: expected value formula)

b. What is the chance that exactly 3 of the customers would purchase at least one item?

c. What is the probability that no more than 3 customers would purchase at least one item? (Hint:

sketch a table for the number of people who would purchase at least one item out of the 10.

You do not need to put in all the probabilities, just all the values of X. For which values of X

would you have to add the probabilities? Student who were in my BUS 90 class are familiar with

this problem. Feel free to help your fellows on Canvas discussion this weekend.)

Binomial again

You are in charge of setting up a lunch with 4 of your friends. You have agreed to buy a take-out lunch at

a small café that makes sandwiches. Todays daily specials are a turkey sandwich and a club sandwich

(but more interesting than our first introduction to LPs recipe). Suppose they order the type of

sandwich independently, and the chance of ordering a turkey sandwich is 0.6.

a. What is the chance that all 5 of you (you and 4 friends) order turkey sandwiches?

b. What is the chance that NONE of the 5 of you order turkey sandwiches?

c. How many turkey sandwiches would you expect to order (hint: E(X))

d. What is the chance of ordering exactly the expected number of turkey sandwiches?

(you have to solve c first)

e. What is the chance that at least 4 of you order sandwiches?

3. Uniform

A package delivery service breaks up its shipping charges into weight classes, where the package

weights are uniformly distributed WITHIN each weight class.

a. Suppose one of the shipping classes is 12 to 15 lbs. What proportion of packages in this class

would weigh less than 14 lbs?

b. What proportion would weigh more than 12.5 lbs?

c. What would the average weight for a package in this class be?

4. Uniform distribution

The scheduled commuting time on the Long Island Railroad from Glen Cove to New York City is 65

minutes. Suppose that the actual commuting time is uniformly distributed between 64 and 74

minutes.

a. What is the probability that the commuting time will be less than 70 minutes? (draw the graph

and shade in the appropriate area!)

b. What is the probability that the commuting time will be between 65 and 70 minutes? (draw the

graph and shade in the appropriate area!)

c. What is the probability that the commuting time will be greater than 65 minutes? (draw the

graph and shade in the appropriate area!)

d. What is the expected (average) commuting time?

5. Uniform again

A study of the time spent shopping in a supermarket for a market basket of 20 specific items showed an

approximately uniform distribution between 20 and 40 minutes.

a. What is the probability that the shopping time will be between 25 and 30 minutes? (draw the

graph and shade in the appropriate area!)

b. What is the probability that the shopping time will be less than 35 minutes? (draw the graph and

shade in the appropriate area!)

c. What is the probability that the shopping time will be more than 27 minutes? (draw the graph

and shade in the appropriate area!)

d. What is the mean shopping time?

6. Practice with normal draw graphs with correct area shaded in and proper x and z axes. Use the

tables I handed out in class. If you do not have such tables, google a set to use. To have tables

similar to those I gave you, go back to the assignment where one is attached.)

The fill amount in 2-liter soft drink bottles is normally distributed with a mean of 2.0 liters and a

mean of 0.05 liters. If bottles contain less than 95% of the listed net content (i.e., less than 1.90

liters) the manufacturer may be subject to penalty by the state office of consumer affairs.

Bottles that have a net content above 2.10 liters may cause excessive spillage upon opening.

What is the probability that a randomly selected bottle will contain:

a. Between 1.90 and 2.00 liters?

b. Between 1.90 and 2.10 liters?

c. Below 1.90 liters or above 2.10 liters?

d. About least how much soft drink (in liters) is contained in 99% of the bottles?

e. 99% of the bottles contain an amount that is between which two values, symmetric about the

average?

…

Purchase answer to see full

attachment

Why Work with Us

Top Quality and Well-Researched Papers

We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.

Professional and Experienced Academic Writers

We have a team of professional writers with experience in academic and business writing. Many are native speakers and able to perform any task for which you need help.

Free Unlimited Revisions

If you think we missed something, send your order for a free revision. You have 10 days to submit the order for review after you have received the final document. You can do this yourself after logging into your personal account or by contacting our support.

Prompt Delivery and 100% Money-Back-Guarantee

All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. In case you cannot provide us with more time, a 100% refund is guaranteed.

Original & Confidential

We use several writing tools checks to ensure that all documents you receive are free from plagiarism. Our editors carefully review all quotations in the text. We also promise maximum confidentiality in all of our services.

24/7 Customer Support

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

No need to work on your paper at night. Sleep tight, we will cover your back. We offer all kinds of writing services.

Essays

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.

Admissions

Admission Essays & Business Writing Help

An admission essay is an essay or other written statement by a candidate, often a potential student enrolling in a college, university, or graduate school. You can be rest assurred that through our service we will write the best admission essay for you.

Reviews

Editing Support

Our academic writers and editors make the necessary changes to your paper so that it is polished. We also format your document by correctly quoting the sources and creating reference lists in the formats APA, Harvard, MLA, Chicago / Turabian.

Reviews

Revision Support

If you think your paper could be improved, you can request a review. In this case, your paper will be checked by the writer or assigned to an editor. You can use this option as many times as you see fit. This is free because we want you to be completely satisfied with the service offered.