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STAT 362

Spring 2020

Homework 5

Problems

DUE DATE: WEDNESDAY, FEBRUARY 5, 2020 by 11:59 PM on Gradescope

Grading:

• Part 1: Swirl Module will be graded.

• Part 2: 5 randomly selected problems will be graded. The rest of the problems will be taken

for completion points only.

This homework has a total of 18 problems.

Part 1: Swirl Module

1. In the console window where you can type in R code, type the following to load swirl:

library(swirl)

swirl()

2. R will ask you for your name. Type your name.

Follow the prompts on the screen. To exist swirl, press the Esc key. If you are already at the

prompt, type bye() to exit and save your progress. When you exit properly, you’ll see a short

message letting you know you’ve done so.

3. Complete Module 13: Simlulation.

After completion

• When they ask “Would you like to receive credit for completing this course on

Coursera.org?”, type YOUR NAME (FIRST AND LAST).

• Hit enter.

• Print the screen. This shows that you have completed the assignment.

• Then for selection, type “0”.

4. Upload your screenshot as part of your Homework 5 submission.

Part 2 Directions: For the following, report your code as well as your final answer.

Part 2 Problems:

1. Suppose you want to make a password using exactly 4 out of the 6 letters: e, t, a, b, p, k.

You do not want to repeat any letter. How many different passwords can you create?

2. In a poker hand consisting of 5 cards, find the probability of holding 4 hearts and 1 club.

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3. An automatic welding machine is being considered for use in a production process. It will

be considered for purchase if it is successful on 99% of its welds. Otherwise, it will not be

considered efficient. A test is to be conducted with a prototype that is to perform 100 welds.

The machine will be accepted for manufacture if it misses 3 welds or less.

(a) What is the probability that a good machine will be rejected?

(b) What is the probability that an inefficient machine with 95% welding success will be

accepted?

4. Find P(X ≤ 813) assuming:

(a) X ∼ Bin(2000, 0.4)

(b) X ∼ N(µ = 800, σ 2 = 480)

5. Suppose X follows a continuous uniform distribution from 1 to 5. Determine the conditional

probability P(X > 2.5 | X ≤ 4). Hint: see Definition 2.10 from the Stat 381 textbook.

6. Given a standard normal distribution, find:

(a) the area under the curve that lies to the left of z = 1.72.

(b) the area under the curve that lies between z = −2.16 and z = −0.65.

(c) find the value of k such that P(Z < k) = 0.0427.
(d) find the value of k such that P(Z > k) = 0.2946.

7. The finished inside diameter of a piston ring is normally distributed with a mean of 10 centimeters and a standard deviation of 0.03 centimeters.

(a) What is the probability that piston ring will have an inside diameter between 9.97 and

10.03 centimeters?

(b) Below what value of inside diameter will 15% of the piston rings fall?

8. Find:

(a) the 95th percentile from a Standard Normal Distribution.

(b) the 90th percentile from a Standard Normal Distribution.

(c) the 99th percentile from a t-distribution with 13 degrees of freedom.

(d) the 95th percentile from a t-distribution with 9 degrees of freedom.

9. Generate 30 values from the interval [50, 200] allowing for repeats. Use a seed of 18. Report

the mean and standard deviation of your sample.

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