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18.05 | Spring 2014 | Undergraduate

# Introduction to Probability and Statistics

### Reading Questions Answer Checker

To check your answers put them in the appropriate box and click the ‘Check’ button. Every checker box can do arithmetic and calculate standard functions (see calculator help). If you give decimal answers, give them to at least 3 decimal places.

As you work you should have pencil and paper handy for calculations and thinking!

Note: some questions ask for a formula. For the checker we ask you to plug a value into the formula. For your pset you still need to give the whole formula.

//DEBUG PARAMETERS //Because we don’t show solutions for pset checkers we use //this to give a showanswer button during the debugging phase var debugans = undefined; //release //var debugans = kDebugAnswer; //debug problemNumber = 0; wl("<h3>Calculator</h3>"); writecalculator(“psetcheckcalcid”, “Calculate”); whr(kdivcol,kdivwid);

//Problem 1 problemNumber++; wl(problemheader(problemNumber)); var s; var partName, problemName, buttonLabel, answerArray, correct; s = [‘In these problems we want you to estimate probability intervals for various quantities. This is best described by example.’, kp, boldtext(‘Example.’) + ’ Give your 50% probability interval for the median family income in Hungary. Do this by specifying the 25% lower bound and the 75% upper bound. Do not look anything up on the internet. Just make your best guess based on what you already know. There is no single correct answer.’, kp, boldtext(‘Answer.’) + ’ The question asks me to give a lower bound $L$ and an upper bound $U$ so that I think/feel/believe that there is a 25% chance the true value is less than $L$ and a 25% chance the correct vaue is greater than $U$. This leaves a 50% probability the true value is between $L$ and $U$. ‘, kp, “Well let’s see. I seem to recall the median income in the U.S. is about \\$50,000. I’ll guess that Hungary is quite a bit lower, maybe around \\$32000. I’m not all that confident it’s not quite a bit lower than that. So my guess is that the 25% lower bound is \\$19,000 and the 75% bound is \\$40,000.”]; wl(s.join(’ ‘)); wl(kp); s = [“Now it’s you’re turn. Without looking anything up online give your 25% lower bound and 75% upper bound for each of the following quantities.”, kp, “Answers we culled from the internet will be in the solution slides for this class.”]; wl(s.join(’ ‘)); wl(kp); s = “(a) The total number of airline deaths in the last 100 years.”; wl(s); wl(kp); s = “25% lower bound.”; wl(s); wl(kbr); partName = problemNumber + " (a.i)"; problemName = “prob” + partName; buttonLabel = “Check problem " + partName; writeNumericBox(partName+“id”, 500000000, buttonLabel, 500000000, kNoShowAnswer); wl(kp); s = “75% upper bound.”; wl(s); wl(kbr); partName = problemNumber + " (a.ii)”; problemName = “prob” + partName; buttonLabel = “Check problem " + partName; writeNumericBox(partName+“id”, 500000000, buttonLabel, 500000000, kNoShowAnswer); wl(kp); s = “(b) The number of girls born in the world each year.”; wl(s); wl(kp); s = “25% lower bound.”; wl(s); wl(kbr); partName = problemNumber + " (b.i)”; problemName = “prob” + partName; buttonLabel = “Check problem " + partName; writeNumericBox(partName+“id”, 500000000, buttonLabel, 500000000, kNoShowAnswer); wl(kp); s = “75% upper bound.”; wl(s); wl(kbr); partName = problemNumber + " (b.ii)”; problemName = “prob” + partName; buttonLabel = “Check problem " + partName; writeNumericBox(partName+“id”, 500000000, buttonLabel, 500000000, kNoShowAnswer); wl(kp); s = “(c) The percentage (between 0 and 100) of African-Americans in the U.S. population”; wl(s); wl(kp); s = “25% lower bound.” wl(s); wl(kbr); partName = problemNumber + " (c.i)”; problemName = “prob” + partName; buttonLabel = “Check problem " + partName; writeNumericBox(partName+“id”, 50, buttonLabel, 50, kNoShowAnswer); wl(kp); s = “75% upper bound.”; wl(s); wl(kbr); partName = problemNumber + " (c.ii)”; problemName = “prob” + partName; buttonLabel = “Check problem " + partName; writeNumericBox(partName+“id”, 50, buttonLabel, 50, kNoShowAnswer); wl(kp); s = “(d) The number of French speakers world-wide.”; wl(s); wl(kp); s = “25% lower bound.”; wl(s); wl(kbr); partName = problemNumber + " (d.i)”; problemName = “prob” + partName; buttonLabel = “Check problem " + partName; writeNumericBox(partName+“id”, 500000000, buttonLabel, 500000000, kNoShowAnswer); wl(kp); s = “75% upper bound.”; wl(s); wl(kbr); partName = problemNumber + " (d.ii)”; problemName = “prob” + partName; buttonLabel = “Check problem " + partName; writeNumericBox(partName+“id”, 500000000, buttonLabel, 500000000, kNoShowAnswer); wl(kp); s = “(e) The number of abortions performed in the U.S. each year.”; wl(s); wl(kp); s = “25% lower bound.”; wl(s); wl(kbr); partName = problemNumber + " (e.i)”; problemName = “prob” + partName; buttonLabel = “Check problem " + partName; writeNumericBox(partName+“id”, 500000000, buttonLabel, 500000000, kNoShowAnswer); wl(kp); s = “75% upper bound.”; wl(s); wl(kbr); partName = problemNumber + " (e.ii)”; problemName = “prob” + partName; buttonLabel = “Check problem " + partName; writeNumericBox(partName+“id”, 500000000, buttonLabel, 500000000, kNoShowAnswer); wl(kp); whr(kdivcol,kdivwid);

## Course Info

##### Instructors

- Dr. Jeremy Orloff
- Jonathan Bloom

##### Departments

- Mathematics

##### As Taught In

Spring 2014

##### Level

Undergraduate

##### Topics

- Mathematics
  - Discrete Mathematics
  - Probability and Statistics

##### Learning Resource Types

assignment_turned_in Problem Sets with Solutions
grading Exams with Solutions
notes Lecture Notes
co_present Instructor Insights
theaters Other Video

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