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# scan0100 - " AMS310 TEST 1 PAGE 5 OF 7 PRINT YOUR NAME...

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Unformatted text preview: " AMS310 TEST 1 PAGE 5 OF 7 PRINT YOUR NAME HERE \ " LONGER QUESTIONS. FOR THESE QUESTIONS VVHEREVER THERE IS A NUMERICAL ANSWER YOU NEED TO SHOW HOW YOU ARRIVED AT IT. YOUR SCORE WILL BE - DETERMINED BY YOUR PRESENTATION OF YOUR IVIETHOD. “—2. When an opinion poll calls residential telephone numbers at random, only 20% of the calls reach a live person. Suppose the random dialing machine makes 16 calls. Then the number of calls reaching a person, Y is a binomial variable with n=16 and p=0.2. .‘ .., In i, u 3:; (a)(i) What is the mean number calls that will reach a person in samples of 16 random dialed calls? (a)(ii)What is the standard deviation of Y the number of calls reaching a person in samples of 16 randomly dialed calls? “dymngwvnuw- s I”? t.» it? \v t") s. (a)(iii) Let Y” denote the observed number of calls In a sample of 16 that do not reach a person What is the standard deviation of Y‘? 1* = X v If. “in; if.» :W - f.— 1% 3/! ‘ ”I [-2 .5: 12" 1.: (.1, ,3 ». % tax ~47. *‘ > (c ) What Is the probability that less than 10 out of 16 calls will NOT reach a person? /-.j=~ “’ :1: it... 5 .: 5:: 7 (g; 2,; \$1... a) a“ la» 3 my ‘61“; =- (d) We do 16 random dials and note that 7 reach a person. Use your result' In part (b) to comment on whether having 7 or more success in a sample of 16 random calls is an unusual event if p= O. 2. (An event Is unusual Is an event if it has probability less than 0.05). Write at least one sentence indicating your reason for your conclusions. {- ’ V ’r “’ ‘ g) a I‘l- g t". . ”\$1,, . :3” r .‘dv‘xfg r.” 1“,:- v: "a ...
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