!"#"$%&'$%()%*+,-#.%&/,012%#34%!#-5.637%862",69/"6+32$% !1:"6+3%($;)%<,#5'2%+=%*+,-#.%>,+9#96.6"?%862",69/"6+32$% @1#"/,12%+=%"'1%*+,-#.%&/,01% • !"##$%&'()*&+),&-.""*$/(0&+/#1),&!2& • 3(4%*-$&5#()$&,(/*0$'.&+6#7*&!2& • 8%*&01/7*&)*7*/&$#10%*-&$%*&%#/(9#)$+'&+:(-&()&*($%*/&,(/*0$(#)2& • ;-&"&()0/*+-*-<&$%*&01/7*&-5/*+,-&#1$2& • ;-&"&,*0/*+-*-<&$%*&01/7*&6*0#"*-&"#/*&5*+=*,&+/#1),&!2& • >)?'*0$(#)&5#()$-&+$&!&@&"2& & >,+51,"612%+=%A'1%*+,-#.%862",69/"6+3%
&
8%*&01/7*&(-&AAAAAAAAAAAAAAAAAAAAB($%&$%*&%(4%*-$&5#()$&#7*/&$%*&"*+)<&#2& & 8%*&01/7*&(-&AAAAAAAAAAAAAAAAAAAAAAAAAAA&+6#1$&+&7*/$(0+'&'()*&$%/#14%&#2& & 8%*&01/7*&+55/#+0%*-&$%*&AAAAAAAAAAAAAAAAAAAAAAAA&+:(-&61$&)*7*/&$#10%*-&#/&0/#--*-& ($2& & 8%*&$/+)-($(#)&5#()$-&6*$B**)&0155()4&15B+/,&+),&,#B)B+/,&#001/&+6#7*& $$$$$$$$$$$$$+),&$$$$$$$$$$$$2& & &
BC#-5.1%;)%C##=&$#&$%*&)#/"+'&01/7*-&()&$%*&?(41/*&6*'#B2&
&
&
+D E#&$%*-*&,(-$/(61$(#)-&%+7*&$%*&-+"*&"*+)F&>?&-#<&B%+$&(-&($F& & & 6D G)*&#?&$%*&01/7*-&0#//*-5#),-&$#&+&)#/"+'&,(-$/(61$(#)&B($%& ! = 3 &+),&$%*& #$%*/&$#&#)*&B($%& ! = 1 2&H%(0%&01/7*&%+-&B%(0%& ! F&
& & & BC#-5.1%D)%I(7*)&$%*&$B#&)#/"+'&01/7*-<&0#"5+/*&$%*&"*+)-&#?&$%*&$B#&)#/"+'& ,(-$/(61$(#)-2&
&
&
A'1%B-56,6:#.%E/.1% ;55'(*-&#)'.&$#&AAAAAAAAAAAAAAAAA&,(-$/(61$(#)-2&
&
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xample 4: !"#$%&''#'$()$*"#$&+,-*$('*./0"#'$&*$*"#$1/-&'$2(($&.#$3(.%&--4$ !"#$%"&'!"#$%&!'$($)"(*$+,$-./$01$(*#$($2!(*#(3#$#"4&(!&+*$+,$-5$016& !"#$%&'%$"(%)*+,#,&-&$.%$"#$%#%*#/0+1-.N!"#"$%"&'(!%)*$+',*##'+-."'-'/-!!' !"#$""%&'()&*+&,%-&'.)&*+/& !"#$!"#$%& & !"#$%%#&'(& & !"#$!"#$%&& & !"#$%&#'(&
BC#-5.1%H)%8%*&.*+/'.&B%*+$&.(*',&5*/&+0/*&#)&+&5+/$(01'+/&?+/"&(-&)#/"+''.& ,(-$/(61$(#)&B($%&"*+)& µ = 35 &61-%*'-&+),&-$+),+/,&,*7(+$(#)& ! = 8 &61-%*'-2& a. Shade the area under the curve in the figure below that represents the probability that an acre will yield between 19 and 35 bushels.
& b. Is the area the same as the area between µ ! 2" and µ ?
&
& & & c. Find the percentage of area over the interval between 19 and 35. & & d. What is the probability that the yield will be between 19 and 35 bushels per acre? & BC#-5.1%I)%8%*&5'+.()4&'(?*&#?&+&!1)-%()*&/+,(#&(-&)#/"+''.&,(-$/(61$*,&B($%& "*+)& µ = 600 &%#1/-&+),&-$+),+/,&,*/(7+$(#)& ! = 100 &%#1/-2&H%+$&(-&$%*& 5/#6+6('($.&$%+$&+&/+,(#&-*'*0$*,&+$&/+),#"&B(''&'+-$&?/#"&OLL&$#&PLL&%#1/-F&
&
&
&