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.
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