course material

1. Assuming Jerry and Jill play independently, what is the distribution
Stat 311 Quiz 2This 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 theUniversity of Washington.Unless specified otherwise, to receive credit
you must show your work on all computations or give brief explanations, where
appropriate.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.Any probabilities or
quantiles can be found using R. When you use R, be sure to include the code and output.All
final numerical answers should be accurate to two decimal places (nearest hundredth);
however, probabilities should be reported to four decimal places, if applicableAll
intermediate calculations that are not probabilities should be accurate to at least three
decimal places.Do not forget units where applicable.Read each problem carefully and follow
directions. Make sure you answer the question that is asked.When writing or typing out
your solutions, please do NOT squish all your work together. Leave space between
problems and the parts of each problem. Make your answers easy to read! If we cannot
easily ready your work, it will not be graded.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.a) Name the
distribution, with specific parameter values, which can be used to model X.b) Write out the
correct formula, with specific numbers substituted, to find the probability that there is at
most one working battery among the four sampled batteries. Do not solve.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.RatingGenre PG PG-13 R
TotalAction/Adventure 20 15 20 55Comedy 20 22 31 73Documentary 8 11 9 28Drama 20
39 57 116Total 68 87 117 272a) For a randomly selected film what is 𝑃𝑃(𝑅𝑅 ∩ 𝐺𝐺)?b) For a
randomly selected film what is 𝑃𝑃(𝑅𝑅|𝐺𝐺)?c) For a randomly selected film what is

2. 𝑃𝑃(𝐺𝐺|𝑅𝑅)?d) Are the events R and G independent? Justify your answer using an equation
with all the numbers filled in.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.a) If you randomly select one bearing from this population, what is
the probability that the bearing has a diameter less than 4 mm?b) What bearing diameter
separates the largest 6% of diameters from among all diameters from this population?c) A
randomly selected bearing from this group has a diameter of 4.25 mm. What percentile does
this correspond to?d) A random sample of 20 bearings are selected from this population.
What is the probability distribution for the sample mean diameter? Be sure to name the
distribution and the values of any parameters.e) What is the probability that the mean
bearing diameter exceeds 4.26 mm?f) Find the probability that a random sample of 20
bearings has a mean diameter of exactly 4.2 mm.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.a) Assuming Jerry and Jill play independently, what
is the distribution of D? Include the name of the distribution and the values of the
parameters. Show your work.b) What is the probability that Jerry will score higher than Jill
in the next game in the tournament? Summarize your answer in a sentence.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.a) What
is the probability that a randomly selected person tests negative for CMV?b) What is the
probability that a randomly selected person testing negative for CMV is truly CMV
free?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.a) What is the height of the probability density
function?b) Find the mean wait time for placing an order at the drive through window.c)
Find the probability that the time to wait for placing an order is between 5 and 7 minutes.d)
About 75% of the customers are expected to wait at most x minutes. Find x.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.a) Specify the values of any parameters for the
distribution of 𝑋𝑋.b) Write out the formula, with numbers substituted, to calculate the
probability that you observe at least three typos in a random selection of 7 pages, but do not
solve. (1 point) 4Problem 8 (1 point each): A test consists of 32 multiple choice questions
with five choices for each question.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.a) Find 𝜇𝜇 𝑋𝑋 .b) Which of the options below is
the exact probability that you guess correctly on at least 14 questions?1 − ∑ �
32𝑖𝑖 �(0.2)𝑖𝑖

3. (0.8) 32−𝑖𝑖32𝑖𝑖=141 − ∑ �
32𝑖𝑖 �(0.2)𝑖𝑖 (0.8)32−𝑖𝑖13𝑖𝑖=1∑ �
32𝑖𝑖 �(0.2)14 (0.8)1832𝑖𝑖=14∑
�
32𝑖𝑖 �(0.2)𝑖𝑖 (0.8) 32−𝑖𝑖32𝑖𝑖=151 − ∑ �
32𝑖𝑖 �(0.2)𝑖𝑖 (0.8)32−𝑖𝑖13𝑖𝑖=0None of the
above.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.a) What is the sample space for
this two-step game?b) Let 𝐴𝐴 be the event the outcome has a tail. What is the probability of
event 𝐴𝐴?c) Let 𝐵𝐵 be the event the outcome has a red marble. What is the probability of
event 𝐵𝐵?