STAT 344
Homework 2
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Instructions:
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Deadline: September 23, 2022, at 11.59PM through Blackboard as a single PDF.
Handwritten solutions must be scanned and submitted as a PDF file.
Typed solutions are acceptable and must be submitted as a PDF file.
Do not submit hard copies in Class.
Do not submit pictures/Photos as multiple files.
Submissions that do not meet all the following criteria will not be graded:
Your solutions will grade for completeness; all steps must be shown. The solutions are expected
to be of collegiate quality.
Each solution should be:
• Written one question per page
• written darkly.
• Should be easy to follow.
• Must show your work
Be sure that your name in the upper right-hand corner of each page.
See below options for generating a PDF for this exam, Name the file
STAT344HW2_Lastname_Firstname.
Once the PDF has been generated, please view the file to assure its legibility prior to uploading.
You will only be able to upload the file once.
Generating a PDF: Here are some options for generating a PDF:
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CamScanner – PDF Scanner App; free on Android and iOS. You can upload to Google
Drive and Dropbox directly.
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Using “Notes” app on iOS/Apple Devices:
You should practice generating a PDF at least three times prior to the submitting one. Be sure that
the file can be easily viewed on a tablet, iPad, and computer.
I strongly suggest that you create a folder on the device that you will use to store the PDFs for this
course.
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Answer all questions. All questions relates to Chapter 2.
1. Customers who are registered on a corporate Web site are summarized by the type of
shipping contract they use and the number of orders in the previous month. The number
of customers in each category are shown in the following table. Customers are to be
selected without replacement.
Shipping Contract Express Standard Total
No orders
25
15
40
One order
65
44
109
More than one order
44
20
64
Total
134
79
213
Suppose that three customers are selected randomly, without replacement, for a survey.
a. What is the probability that at least two selected customers use express shipping?
b. What is the probability that customers from all three order categories are selected?
2. A committee will be formed with 4 managers and 4 engineers selected randomly without
replacement from 11 managers and 16 engineers.
What is the probability that engineer Jane or manager Mary is on the committee?
3. A bag contains red and blue marbles. Two marbles are drawn without replacement. The
probability of selecting a red marble and a blue marble is 0.28. The probability of
selecting a red marble on the first draw is 0.5.
What is the probability of selecting a blue marble on the second draw, given that the first
marble drawn was red?
4. A large car dealership examined a sample of vehicles sold or leased in the past year. Data
is classified by type (car, SUV, van, truck) and by whether they were a sale of a new or
used vehicle or whether the vehicle was leased.
Suppose a vehicle in the sample is randomly selected to review its sales or lease papers
a.
b.
c.
d.
e.
f.
g.
h.
Find the probability that the vehicle was leased.
Find the probability that a vehicle is a truck.
Find the probability that a vehicle is not a truck.
Find the probability that the vehicle was a car and was leased.
Find the probability that a vehicle was used if it was a van.
Find the probability that the vehicle was a van is it was used.
Find the probability that the vehicle was new or a van.
Find the probability that the vehicle was leased or a truck.
5. Consider the following circuit of 5 identical relays. The probability that any relay works
is .8 and the failures of the relays are independent. What is the probability that, when
current is applied, it flows from point 1 to point 2?
6. Accidents on highways are one of the main causes of death or injury in developing
countries and the weather conditions have an impact on the rates of death and injury. In
foggy, rainy, and sunny conditions, 1/4, 1/8, and 1/21 of the accidents result in death,
respectively. Sunny conditions occur 60% of the time, while rainy and foggy conditions
each occur 20% of the time.
Given that an accident without deaths occurred, what is the conditional probability that
it was foggy at the time?
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