StatisticsMathl2l.A2More Probability ProblemsDr. PendergrassSpring 20092.print name:ON MY HoNoR, I HAVE NEITI{ER GIVEN NOR RECEIVED ANY AID oN THIS WORK, NOR AM I AWARE OF ANY BREACH OF TTmHONOR Coop TTI T I SHALL NOT IMMEDIATELY REPORT.pledged:Show your work. This assignment is due at the beginning of class on Thursday, February 26. Wite up yoursolutions neatly, one problem per page, and hand them in with this sheet as a cover page.ISuppose we have anuffiir coin, whose probability of heads is 0.7. We toss the coin 3 times, and record theoutcomes in order. Tosses are still independent, so what we get on toss t has no eflect on toss 2, etc. Writedown the probability model for this experiment as a table. (Hint use independence to calculate theprobability of each outcome.)An urn has 3 red balls and 3 white balls. We pick two balls at random from the urn (i.e. we choose an SRSof size 2). LetNbe the number of red balls chosen. Find the probability model for,n/. (Hint: there are 15possible outcomes to this random experiment.)3 . Below you see the graph of a probability density function p(x) for a certain random variable Xa. What is the value of ft?b. Find P(0.5 <X< 1.5).Suppose the heights of Hampden-Sydney students are normally distributed, with mean 69 inches andstandard deviation 2.9 inches. Pick a Hampden-Sydney student at random, and let I/be his height. FindP(H> 76).Calvin's favorite cereal, "Chocolate Coated Sugar Bombs", comes in a standard box that is labeled ascontaining 32 ounces of cereal. However, there is some variability in the actual amount of cereal that windsup in a box. The manufacturers know that the standard deviation of the amount of cereal in a box is o =25ounces. How much cereal should they actually put in the boxes on average @) in order for the probabilifythat a box contains less than 32 ounces be only 0.5Vo?4.5.--b,l ,tt'-,,U.o 1)" ta,oil =o 1)" (og) =\/tInr][N4\'L\r'.1\v,/t =&r c rrLa"yk\+-rt^bftL-lil"(u g)( 0:iQr) lor\4[.,r) (a j)L&L L;t-V-,bn d"iA-TAA-il1t-tt-t< t1-'fli-t \T {i1-r {\(rLt\./ -) uh,fq-l---_1r__-----\t'7/h,J(ttL--/'r2b,14,^ -\/ =\J't Ilo t\1r\ule I+Ou Lcttl",\e-(:rNz-zl*II-1JIII;II;;ol(-Llt9t/$t{nt/rql6t/vzLlfi4,1U1tltqv,/192!1+w3!49L/6tlv_t/ vr/ t4vvLf .5t/v,6t/F^bJ,l','l'/,ln-C;t^l l'lrco' =( A,, f,r',)+1O'\I+ ,^.tt,) k2 t^.ta-lzn/=lX:a-4rJ1-42\ ,nt,-L+L+'7=1\LWqz7l*t/1L.7-<,'ll \ - jY1,7."<):D'ooyInn Nor"^ [ o.oo9, o, )\ )b'.,'1ft),rL^ N'TL, (- ,2,5) = -2-51E5v)- t=gfo*s u=dD br64h["- Ltr'tc<=\n-[--Jo1a iM , -75-t5h-L.t0'\f ^ -l \/^ 'n lL+ L I0q1' l )= 14' q4tt1,
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