Exam 2 Review KEY - Exam 2 Review 1(a What Is the...

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Unformatted text preview: Exam 2 Review 1. (a) What Is the definition of statistic? NU‘MOftCQ\ (\i‘yqucjtcfdw Q“; q Sqmwfi (b) State 3 different statistics and give the notation corresponding to each of them. Statistic (in words) Notation (Symbol) quele: s—lol olev s l 3:0 wig _§ l-ZE _l/\ 2. (a) What iS the definition of parameter? NUMQfI UK\ CkOI/mCJlQ/U‘JL 5“? °\ (PU (All \‘fifi‘io’m (b) State 3 different parameters and give the notation corresponding to each of them. Parameter (in words) Notation (Symbol) Apt/16AM 1mm 1/1; 0% u all Im > D if go p— j (15% 3. Aperson rolls two fair dice. What Is the probability the sum ofthe values ofthe sides facing up is 5? 3% O‘UVWQS . I . ,V t of 6‘? {Cl ‘3‘) HID (743) {3/93 50m 4 D 0 .. //, 4\\\ 4. Table below shows results of polygraph test given to subjects. Lied Did Not Lie Positive Test Result 79 _l 28 True Positive False Positive Negative Test Result 13 61 False Negative True Negative (3) What is probability that a randomly selected subject had a negative test result or did not lie? , ’\ _ l3~i€l +2? ._ \oz: P C“— Q r M) “ 13+ c l +- 23 + it a i if“! :m?’ (b) What is the probability that a randomly selected subWive test resultunngdm.‘.7.__.s..v.‘_i.__\ r C + M a}: 13?; 3 Mi) ‘\ \ (c) What is the probability that a randomly selected subject had a negative test/em‘TgivenJgey lied? m "_,.,..»~—-~ \ ‘3 \7) \ V i‘ l. ¥~ .5- i \P ( w— ‘ L.) x l 3 Jr Ti ‘3 9 Z. ‘0 1 ?“ (d) What is the probability that a randomly selected subject lied given they had a negative test result? ' ”a , \3 _7 :Efi ) “"”“\ F (L ’ "3‘ lBtSl Riff/"l:{\§‘)flfl) 5. For each attempted free—throw basketball shot John attempts, the probability of making the shot is 0.6 and each attempt is independent of the previous attempts. For each attempted free-throw Susie attempts, the probability she makes the shot is 0.8 and each attempt is independent of the previous attempts (also assume that the events John makes a shot and Susie makes a shot are independent of each other). (a) if John and Susie attempt one shot each, what is the probability John will make the shot or Susie will make the shot( at least one of them makes the shot)? ‘“ / SB:- “5% 9(5) 1 “WWW (9(0 6 ,_. PC3071 9(5) ‘“ ?CT)“€(5) mm 1 . {Aria/:30? ”9h 6% : ots i o.8~ Cod/0.3) 4‘0 ‘1 L (b) If John attempts five shots, what Is the probability John will make at least one shot? x: hb‘lJ Tohh mslfit’j (be I): in HM»: :: j~—C©fiff’: (0990“ > BONUS: A clinical test on humans of a new drug is normally done in three phases. Phase I is conducted with a relatively small number of subjects. For example, a phase I test of bexarotene involved 13 subjects and there are 16 suitable volunteers If 13 subjects are randomly selected from the 16 volunteers, what Is the probability of selecting the 13 youngest of tljalavolunteers? 6. Determine whether the following table is a probability distribution or not. if it is, show that it satisfies all the requirements of a probability distribution. If it is not, show why not by showing at least one requirement that it violates. 7. Determine whether the following table is a probability distribution or not. If it is, show that it satisfies all the requirements of a probability distribution. If it is not, show why not by showing at least one requirement that it violates. 8. The following table represents the probability distribution of road worthiness of Chevrolet trucks that are 3 years old. The random variable x represents the number of cars thatfai/ed among a batch of five that were tested for roadworthiness. x P (x) _I____l O 0.42 _J__ 1 0.38 2 0.12 #307 flag] (a) What Is the probability that exactly 3 of the 5 trucks fail the test? (c) ls 3 anu unusually high hnumber of trucks out of a batch of 5 to fail the test? (Justify answer) €(x: :5 (l3 <é©f5 ....... _......,._.~. ,fa— : <Jo¢*looz+0biv g): Q®3\7CLO§ not onmm/ly hlfh (d) Would it be unlikely for 3 trucks out of a batch of 5 to fail the test (justify answer). 9Q: ~g\ : 004 Logo; EKWNWW ElNOwAL 9. Suppose 70% of the student population of UC Davis have brown eyes. For all of the following parts in this question, assume a random sample of 12 UC Davis students has been selected. (a) What is the probability that exactly 11 of them have brown eyes? (OsXO: wCU&x®“QLfi‘ :(égEffip (b) What is the probability that at least 11 of them have brown eyes? V(2\<—2ll§ -: ly(ltlhl WWW/j ) ~ - 4 run 3<3oqp;%iLCa([email protected] Lall /,,-"’ ””” M I‘ r) “.1 ,_.; _ r" d r S B t: voM~llP¢\L(G§—r fig (d) What is the standard deviation of number of UC Davis students with brown eyes? ezmr—CQ (e) ldentify all distinct ossible values from the sample of 12 students that would be unusual for number of students with brown eyes from the sample. min 05ml :: M“ Z/LS": §flr¢¢Cis€l=52 mm Meal 1 Mini : fi‘f+2(lb€3:“»€ 10. The birth weights of U.S. babies have a normal distribution with a mean of7.4 pounds and standard deviation of 1.3 pounds. (a) Find the probability that a randomly selected baby will have a birth weight less than 8.0 pounds. fl Q\[l/\‘/\§A\ P[ X 4 8‘»: 6) (: 4 O 4&3 {096‘}? Z; - ..... .\ (b) Find the probability that a random sample of 12 babies will have a sample meafibir'th'WeIght less than 8.0 pounds. ...
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