Stat 311 Quiz 2
This is an untimed quiz that must be completed and uploaded before the end of the window. This quiz is open Stat 311 notes, textbook, and homework/solutions only. All responses must be your own. If I suspect that you collaborated with other people or put down answers that match something you found on the internet, your quiz score will be zero and I will file a report with the Student Conduct office. By uploading your quiz to Gradescope, you are acknowledging that you adhered to the rules and academic conduct standards set by the
University of Washington.
o You will be graded only on the work you show.
o Partial credit may be given when you show the process used to solve a problem, even if your answer is incorrect.
o You only need to summarize answers in sentences where specified.
The quiz consists of 9 multi-part problems. Each part of every problem is equally weighted.
2Problem 1 (1 point each): A junk box in your room contains 16 old batteries, 6 of which are dead. Define the random variable X = the number of working batteries in a sample of 4 batteries from the junk box.
Problem 2 (1 point each): The table below summarizes 272 films from 2011 that have been classified into a genre and have a rating. Define the events R = Rating PG-13 and G = Comedy. Use events R and G and the table below to answer parts(a) – (d). Show your work and summarize your answers in a sentence in the context of the problem.
Genre PG PG-13 R Total
Action/Adventure 20 15 20 55
Comedy 20 22 31 73
Documentary 8 11 9 28
Drama 20 39 57 116
Total 68 87 117 272
Problem 3 (1 point each): A machine operation produces bearings whose diameters are normally distributed with 𝜇𝜇 = 4.2 mm and 𝜎𝜎 = 0.08 mm. Use R to find probabilities and quantiles, as appropriate. For any problems where you use R, be sure to include the code and R output. Summarize each answer in a sentence in the context of the problem.
3Problem 4 (1 point each): Jerry and Jill are playing in a bowling tournament. Their scores vary as they play multiple games. Jerry’s scores, X, follow a 𝑁𝑁(𝜇𝜇 = 208, 𝜎𝜎 = 7) distribution. Jill’s scores, Y, vary from game to game according to a 𝑁𝑁(𝜇𝜇 = 200, 𝜎𝜎 = 9) distribution. Define a new random variable 𝐷𝐷 = 𝑋𝑋 – 𝑌𝑌 for a single game in the tournament.
Problem 5 (1 point each): A study concluded that among people infected with Cytomegalovirus (CMV), 98.1% of tests were correctly positive, while for people not infected with the virus, 97.6% of the tests were correctly negative. We also know that 20% of people carry the virus.
Problem 6 (1 point each): Define X to be the time to wait for placing an order at a drive through window and assume X follows a continuous uniform distribution between 0 and 11 minutes. Include units as appropriate.
Problem 7 (1 point each): The number of typos per page in a certain printing of a novel has an average of 1.2 typos/page. Let 𝑋𝑋 be the number of typos in a random selection of 7 pages and assume 𝑋𝑋 follows a Poisson distribution.
As an experiment, you GUESS on each answer without even reading the questions. Define X to be the number of questions you get correct based on guessing and assume X follows a binomial distribution. Use this information to answer parts (a) and (b). Include units where appropriate.
𝑖𝑖 � (0.2)𝑖𝑖 (0.8) 32−𝑖𝑖32
𝑖𝑖 � (0.2)𝑖𝑖 (0.8)32−𝑖𝑖13
𝑖𝑖 � (0.2)14 (0.8)1832
𝑖𝑖 � (0.2)𝑖𝑖 (0.8) 32−𝑖𝑖32
𝑖𝑖 � (0.2)𝑖𝑖 (0.8)32−𝑖𝑖13
Problem 9 (1 point each): A game is played in two steps. First you flip an unfair coin with 𝑃𝑃(𝐻𝐻) = 0.6. If you get heads, you draw a marble from an Urn that has 6 red marbles and 4 blue marbles. If you get tails, you flip the coin again.
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