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UW-Madison STAT 301 - Assignment #3 Probability

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Stat 301 Spring 2021Assignment #3 — Due Friday, February 26 at 11:59 pm20 Points Total: 4 Points completeness, 16 points correctness*Submit your homework to Canvas in a single p df before the due date. No late homework will be accepted forcredit!*On the top of the first page, remember to write your name.*If a problem does not specify how to compute the answer, you may use any appropriate method.*Explanation or work must be shown to recei ve full credit. The gradi ng TA will grade for c orr ec t ne ss and clarity.*Recommended reading: FPP Chapters 13, and 14.0.1 Textbook Exercises1. From the book: Chapter 13 Review Exercises (pages 234-236), exercises: 3, 5, 7.2. From the book: Chapter 14 Review Exercises (pages 252-254), exercises: 9, 12 (Hint: for 9, list out theoutcomes you want and compare them to the total possible outcomes.)0.2 Non Textbook Exercises3. An electronics store kept records of sales of tablets for the previous month. Those buying a tablet had theoption of bu y in g an additional warranty for their ite m. It was also recorded whether the customer paid withcredit card or cash ( no other payment methods were allowe d) . Some summary information is below. Pleaseanswer the questions below the table. It may help to orgaize the information into a two-way table.Category NumberTablets purchased with credit card 122Tablets sold with warranty 36Tablets sold with warranty purchased wit h cre di t card 24Total tablets sold 200(a) What percentage of tablets were purchased with cash?(b) What percentage of tablets were sold without the warranty?(c) What percentage of tablets purchased with cash were sold with the warranty?(d) What percentage of tablets sold with the warranty were purchased with cash?(e) What percentage of all tablets sold were purchased w it h cash and without a warranty?1Deysiachase-r-.IStat 301 Spring 2021(f) Are paying with cash and buying the warranty independent events? Why or why not?(g) Suppose you build a box model to desc r ibe the situation above and chose two tickets with replacement.What is the chance that both draws are tickets where the tablet was purchased with cash?4. Suppose you can somehow choose two people at random who took the SAT in 2014. Scor es were normallydistributed wit h mean and stan dar d deviation of 1497 and 322, respectively. What is the probability thatboth of them scored above a 1520? Assume that the scores of the two test takers are independent.2TextbookExercisesChpt133)Optioniiisbetterbecausetherearemultipleway stowin.Thecardsonlyhav etobedifferentsuits,notinanypar ticularorder.5)Colorandnumberareindependent.f-=L--is(own?)¥=%=-67(1)-5x.67=-347)Ciscorrectbecausebothsequencesareequallylikelyflipisindependent.>!:3?"b)I-I,2-2,3-33I25%32-3334c)I-2I-3I-42-32-950%3-412a)True.12b)True.Afterthefirstninetosses,thechanceisso-sofortheLothhead.NonTextbookExercisesSa)78/200=39%cashCCTotalW122436mW66981643D-164=821.-200Total781222003D¥=-1538=15.4%3d)12=33.3%363e)led=331.2003f)Theyarenotindependent.Thetablethastobepaidforbycardorcash,withtheoptiontobuythewarranty...nomatterhowyoupay.3g).39..39=15.2chance-Cbotnchancesthatareindependent)4)-0.

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