College of Engineering
NGN 29402 – Applications of Probability and Statistics in
Engineering
Fall 2024
HW – 1
Due: September, 22nd
Student Name
ID No.
Section No.
Total Marks out of 100
Homework Submission Guidelines
Please adhere to the following submission guidelines:
1. Detailed Work Required: All submitted homework must include
detailed steps of your work. Submissions that only contain the final
answers will not be graded.
2. Format of Submission: Homework must be submitted as a SINGLE
PDF file. Ensure that all pages are included in one document and that the
file is correctly formatted and readable.
3. Cover Page Requirement: Each submission must include this page as
the cover page. Ensure that the cover page is the first page of your PDF
file.
4. Organize Your Work: Organize your submission, answers to be in order
and the numbered accurately.
Failure to follow these guidelines may result in your homework not being
graded.
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Question 1:
In a factory that monitors the quality of electronic components, it's observed
that 5% of legitimate components fail tests in any given production stage in a
single day. However, 35% of defective components fail tests at any given
stage on the same day. The overall proportion of defective components is
0.03%. If a component fails in any production stage in a single day, what is
the probability that it is defective?
Solution:
Question 2:
An AI-based system is designed to filter out fake reviews from genuine ones
on a product website. The word "guarantee" appears in 70% of the fake
reviews and only 5% of the genuine reviews. Assume that 15% of the reviews
are fake. Determine the following probabilities:
a. The probability that a review contains "guarantee."
b. The probability that a review is fake given that it contains "guarantee."
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Solution:
a.
b.
Question 3:
An automobile service facility specializing in engine tune-ups has statistical
data on the engine types they work on. The distribution of engine types based
on the number of cylinders is as follows:
45% of tune-ups are done on four-cylinder automobiles.
40% on six-cylinder automobiles.
15% on eight-cylinder automobiles.
a. Determine the cumulative distribution function (CDF) of the number of
cylinders in cars coming in for tune-ups.
b. Determine the mean and variance of the number of cylinders in cars coming
in for tune-ups.
Solution:
a.
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Number of
cylinders X
4
6
8
CDF
0.45
0.45+0.4 = 0.85
0.45+0.4 +0.15=1
b.
Mean:
Variance:
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Question 4:
Thickness measurements of glass sheets produced in a manufacturing process
are measured in millimeters. The thickness measurements of the glass sheets
are uniformly distributed from 20 to 27 millimeters.
Determine the mean and variance of the glass sheet thickness for this process.
Solution:
Mean:
Variance:
Question 5:
When circuit boards used in the manufacture of compact disc players are
tested, the long-run percentage of defectives is 5%. Let x= the number of
defective boards in a random sample of size 25
a. What is the mean value of X?
b. What is the probability less than 3 being defective:
c. What is the probability of exactly 4 being defective:
Solution:
a.
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b.
c.
P(X=4) = 0.0269
Note, Show detailed workings for all questions.
Reference: D. Montgomery, Applied Statistics and Probability for Engineers, 7e, Wiley, 2018
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