Statistics 412: Homework #2
Due Wednesday, September 10
You must show all work when answering the questions as modeled during the lectures. If the answer to the question is
a calculation, be sure to write down the formula, then plug in the values, and only then state the answer. Also, be sure
to include your R, JMP, or any other data analysis package output if you used technology, or you can perform
computations and construct plots by hand.
Note: Homework must be submitted through Gradescope by 10:00PM on the due date. Submission process may take time.
It is recommended that you submit your Homework at least one hour before the deadline. You may also submit partial
work, and later (but before the deadline) submit an updated file. Only the latest submitted file is saved in GradeScope.
Note: When we grade homework, we see each page of your solutions within about 1/2 of the screen. We would
appreciate it if you use high-contrast writing tool (e.g., black pen on white paper), and size/position your writing so that
we don’t have to zoom it in and out. With grading many submissions, it will make a big difference. Please read “About the Images
We Upload to GradeScope” at the bottom of this assignment before you start writing your solutions. Thank you.
1. Compare your HW 1 solutions to the solutions posted on canvas. Solve each problem for which your solution differs
from the solution posted on canvas, regardless of your score, by following the template:
1) For Question __1(a)__ the difference between mine and posted solution is: __ (describe you did differently) __.
This ___ IS ___ IS NOT a mistake because __ (justify your “IS” statement, or provide the correct solution) __.
This material was covered in the __(on what date, e.g., Thursday May 8)__ lecture.
2) . . .
Do this for each question on your list.
2. Section 2.3, Exercise 26: “A certain delivery service offers both express…” (page 87)
3. Section 2.4, Modified Exercise 4: “Let X represents the number of tires…” (page 112)
a. As in the original question (“possible” is the same as “valid”).
b. Find the probability that a randomly selected car has at most three tires with low air pressure if it
has at least one tire with low air pressure.
4. Section 2.4, Exercise 10: “Candidates for a job are interviewed one by one…” (page 113)
Note: This is introduction to Geometric distribution. Pretend that the pool of candidates is infinite, and interviewing one
candidate does not change the probability of finding a qualified candidate in the future interviews. In other words, this problem
can be read as “A coin that lands “Heads” with probability 0.30 is flipped repeatedly”.
5. Section 2.4, Exercise 12 parts (a) – (g): “Three components are randomly sampled, one at…” (page 114)
Note: This is introduction to Binomial distribution. Pretend that the number of components is infinite, and whether or not one
component passes the test does not affect the probability that any of the remaining components would pass the test.
6. Section 2.4, Exercise 8: “After manufacture, computer disks are tested for…” (page 113)
7. Section 2.4, Exercise 2: “Computer chips often contain surface imperfections…” (page 112)
8. Section 2.4, Exercise 12 parts (h), (i), (j): “Three components are randomly sampled, one at…” (page 114)
Note: This is introduction to Binomial distribution. Pretend that the number of components is infinite, and whether or not one
component passes the test does not affect the probability that any of the remaining components would pass the test.
Homework 2, page 1
About the Images We Upload to GradeScope:
Want to peek at how we, as graders, see your uploaded solutions, and at our joys and our pains of grading?
Here are two versions of the uploads (each is a full-screen screenshot):
1. A deliberately over-exaggerated bad version (notice the rubric items on the right!):
2. And a good version:
As you see, on our end your uploaded images appear within only about a quarter of the screen,
so we would appreciate you giving a bit of consideration to the rubric items in these two pictures.
Thanks for keeping this in mind!
Homework 2, page 2