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<span class="katex"><span class="katex-mathml"></span><span class="katex-html"><span class="base"><span class="strut"></span><span class="mop op-symbol small-op">∑</span></span></span></span></span> P(x)=1 which is not true in a and d. In c one P(x)= -0.1 but we know 0≤P(x)≤1 )</p> <p>2) it should be approximately normal with mean 2.8 and standard deviation 0.4 (Since sd =<span class="ql-formula" data-value="\sigma"><span class="katex"><span class="katex-mathml"></span><span class="katex-html"><span class="base"><span class="strut"></span><span class="mord mathdefault">σ</span></span></span></span></span> /<span class="ql-formula" data-value="\sqrt{n}"><span class="katex"><span class="katex-mathml"></span><span class="katex-html"><span class="base"><span class="strut"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="svg-align"><span class="pstrut"></span><span class="mord"><span class="mord mathdefault">n</span></span></span><span class="pstrut"></span><span class="hide-tail"></span></span></span></span></span></span></span></span></span></p> <p><span class="vlist-s"></span><span class="vlist-r"><span class="vlist"></span></span> ). However i don't find this in any option.</p> <p>3) X: for lateness in hours</p> <p>On time means X =0</p> <p>E(X)= <span class="ql-formula" data-value="\sum"><span class="katex"><span class="katex-mathml"></span><span class="katex-html"><span class="base"><span class="strut"></span><span class="mop op-symbol small-op">∑</span></span></span></span></span>x P(x) = 0(4/5) +1(1/10)+2(1/20)+3(1/20) = 7/20</p> <p>4) a) 7C2 = 7!/(2! 5!) = 21</p> <p>b) 7×6 =42</p> <p>c) 7×7 =49</p> <p>1) 1) (4/13)(4/13) =16/169 = 0.09467455621 (with replacement)</p> <p> 2) (4/13)(3/12)=12/156 = 0.076923 (without replacement)</p> <p>6) The table is as follows:</p> <p> F M T</p> <p>S 80 55 <b>135</b></p> <p>N 120 XX <b>165 </b></p> <p>X <b>XXX </b> <b>100 XXX</b></p> <p>a) X(S) = 135/300</p> <p>b) P(F or N) = P(F<span XXXXX="ql-formula" XXXX-value="\cup"><span class="XXXXX"><span class="katex-mathml"></span><span XXXXX="katex-html"><span XXXXX="XXXX"><span class="XXXXX"></span><span class="mord">∪</span></span></span></span></span>N) = P(X)+P(N)-X(F<span XXXXX="ql-formula" XXXX-value="\cap"><span XXXXX="XXXXX"><span XXXXX="katex-mathml"></span><span XXXXX="XXXXX-html"><span XXXXX="base"><span class="strut"></span><span class="XXXX">∩</span></span></span></span></span> N) = 200/XXX + 165/300 - 120/XXX = XXX/XXX</p> <p>c) X(S|M)= P(S<span class="ql-XXXXXXX" XXXX-XXXXX="\cap"><span XXXXX="katex"><span XXXXX="XXXXX-XXXXXX"></span><span class="katex-XXXX"><span XXXXX="base"><span class="XXXXX"></span><span class="XXXX">∩</span></span></span></span></span> M)/P(X) =(XX/XXX)/(100/300)=XX/100</p> <p>Note: All the XXXXXXXXXXXXX are XXXXXXXXXX from table</p> <p>7) <span class="XX-XXXXXXX" data-XXXXX="\mu"><span XXXXX="XXXXX"><span XXXXX="katex-mathml"></span><span class="katex-XXXX"><span class="XXXX"><span XXXXX="strut"></span><span class="mord mathdefault">X</span></span></span></span></span> =69.X</p> <p><span XXXXX="ql-XXXXXXX" data-XXXXX="\sigma"><span class="katex"><span XXXXX="XXXXX-mathml"></span><span XXXXX="XXXXX-html"><span class="XXXX"><span class="strut"></span><span XXXXX="mord XXXXXXXXXXX">X</span></span></span></span></span> =2.8</p> <p>a) X(X&XX;XX)= 1-X(X≤XX) = 1-<span XXXXX="ql-formula" data-value="\Phi"><span class="XXXXX"><span XXXXX="XXXXX-mathml"></span><span class="XXXXX-XXXX"><span XXXXX="XXXX"><span XXXXX="strut"></span><span XXXXX="mord">X</span></span></span></span></span> [(XX-69.X)/2.X] = X-<span class="XX-formula" data-XXXXX="\XXX"><span class="XXXXX"><span XXXXX="XXXXX-XXXXXX"></span><span XXXXX="XXXXX-XXXX"><span XXXXX="base"><span class="strut"></span><span XXXXX="XXXX">Φ</span></span></span></span></span>(0.XXXXXXXXXXX) = X-X.7939=X.XXXX</p> <p>b) X(68≤X≤72) = <span class="XX-XXXXXXX" XXXX-XXXXX="\Phi"><span class="XXXXX"><span XXXXX="XXXXX-XXXXXX"></span><span class="katex-html"><span XXXXX="XXXX"><span class="strut"></span><span class="XXXX">X</span></span></span></span></span> [(72-XX.7)/X.X] - <span class="ql-formula" data-XXXXX="\XXX"><span XXXXX="XXXXX"><span class="XXXXX-mathml"></span><span class="XXXXX-XXXX"><span XXXXX="XXXX"><span class="XXXXX"></span><span class="mord">X</span></span></span></span></span> [(XX-XX.7)/X.8] = <span XXXXX="ql-formula" XXXX-value="\Phi"><span class="XXXXX"><span class="XXXXX-mathml"></span><span class="katex-XXXX"><span class="base"><span XXXXX="strut"></span><span class="XXXX">X</span></span></span></span></span>(0.82142857142) -<span class="XX-XXXXXXX" XXXX-value="\XXX"><span XXXXX="katex"><span XXXXX="XXXXX-mathml"></span><span class="katex-html"><span XXXXX="XXXX"><span class="strut"></span><span XXXXX="mord">Φ</span></span></span></span></span>(-X.60714285714)</p> <p>= <span class="ql-formula" XXXX-value="\Phi"><span XXXXX="XXXXX"><span class="XXXXX-XXXXXX"></span><span class="katex-html"><span XXXXX="XXXX"><span class="XXXXX"></span><span class="XXXX">Φ</span></span></span></span></span>(0.XXXXXXXXXXX)-[X-<span XXXXX="XX-formula" data-XXXXX="\XXX"><span class="katex"><span class="XXXXX-mathml"></span><span XXXXX="katex-XXXX"><span class="XXXX"><span class="XXXXX"></span><span class="XXXX">Φ</span></span></span></span></span>(0.XXXXXXXXXXX)]</p> <p>= <span class="XX-XXXXXXX" XXXX-value="\Phi"><span XXXXX="XXXXX"><span class="katex-mathml"></span><span XXXXX="katex-html"><span XXXXX="XXXX"><span XXXXX="XXXXX"></span><span class="XXXX">Φ</span></span></span></span></span>(0.82) -1+ <span class="ql-formula" data-value="\XXX"><span class="XXXXX"><span XXXXX="XXXXX-mathml"></span><span class="katex-html"><span XXXXX="XXXX"><span class="XXXXX"></span><span class="XXXX">X</span></span></span></span></span>(0.XX)</p> <p>=X.XXXX -1+X.7291</p> <p>=X.XXX</p> <p>8) <span XXXXX="XX-formula" XXXX-value="\mu"><span class="katex"><span XXXXX="XXXXX-XXXXXX"></span><span class="XXXXX-XXXX"><span XXXXX="XXXX"><span class="XXXXX"></span><span XXXXX="XXXX mathdefault">μ</span></span></span></span></span> =101.5</p> <p><span class="XX-XXXXXXX" data-value="\XXXXX"><span class="XXXXX"><span class="katex-XXXXXX"></span><span XXXXX="XXXXX-html"><span class="base"><span class="strut"></span><span class="XXXX mathdefault">X</span></span></span></span></span> =X.X</p> <p>n=XX</p> <p>P(<span XXXXX="XX-formula" data-value="\XXX{X}"><span class="XXXXX"><span XXXXX="katex-mathml"></span><span XXXXX="katex-XXXX"><span class="XXXX"><span XXXXX="XXXXX"></span><span XXXXX="XXXX XXXXXX"><span class="XXXXX-t"><span class="XXXXX-r"><span XXXXX="XXXXX"><span XXXXX="XXXXXX"></span><span class="mord"><span class="XXXX mathdefault">X</span></span><span class="XXXXXX"></span><span class="XXXXXX-body">ˉ</span></span></span></span></span></span></span></span></span>&XX; 102.X)= <span class="ql-formula" XXXX-XXXXX="\Phi"><span class="katex"><span XXXXX="XXXXX-XXXXXX"></span><span XXXXX="katex-XXXX"><span XXXXX="XXXX"><span class="strut"></span><span XXXXX="XXXX">X</span></span></span></span></span> [(XXX.X-101.5)/(1.6/<span class="XX-formula" data-XXXXX="\XXXX{36}"><span XXXXX="katex"><span XXXXX="katex-XXXXXX"></span><span XXXXX="katex-XXXX"><span XXXXX="base"><span class="XXXXX"></span><span class="XXXX XXXX"><span class="vlist-t vlist-XX"><span class="XXXXX-r"><span class="vlist"><span XXXXX="svg-align"><span XXXXX="pstrut"></span><span class="mord"><span XXXXX="XXXX">3</span><span XXXXX="XXXX">6</span></span></span><span class="XXXXXX"></span><span XXXXX="hide-XXXX"></span></span></span></span></span></span></span></span></span></p> <p><span XXXXX="vlist-s"></span><span XXXXX="XXXXX-r"><span class="XXXXX"></span></span> )] </p> <p>= <span XXXXX="ql-XXXXXXX" XXXX-value="\Phi"><span class="XXXXX"><span class="XXXXX-mathml"></span><span class="XXXXX-html"><span XXXXX="base"><span class="strut"></span><span class="XXXX">Φ</span></span></span></span></span> [(X.6)/(X.XXXXX)]</p> <p>= <span class="ql-formula" data-value="\XXX"><span XXXXX="XXXXX"><span class="XXXXX-XXXXXX"></span><span XXXXX="XXXXX-html"><span class="XXXX"><span XXXXX="strut"></span><span class="mord">X</span></span></span></span></span> (2.25)</p> <p>=X.9878</p> <p>X) p=X/X, q=X- X/3 =2/3, n=XX</p> <p>X(X=X) = XXXX (X/X)8 (2/3)30-8 (XXX XXXXXXXX X(X=x)=f(x)=nCx pxqn-x)</p> <p>= 5852925 (0.00015241579)(0.00013365718)</p> <p>=X.XXXXXXXXX</p> <p>b) X(X≥8)= 1-P(X≤X) =f(0)+f(X)+f(X)+f(X)+f(4)+f(X)+f(X)+f(X) where f(x)=nCx pxqn-x with n=XX, x=X,X,2,...,7</p> <p>c) p=X.XX</p> <p>X=0.XX</p> <p>n=XX</p> <p>np = 10</p> <p>npq=20/3 =6.XXX</p> <p>Mean=np ,<span class="XX-formula" XXXX-value="\mu"><span class="XXXXX"><span class="katex-XXXXXX"></span><span class="XXXXX-XXXX"><span class="XXXX"><span class="strut"></span><span class="mord mathdefault">μ</span></span></span></span></span> =XX</p> <p>XXXXXXXX deviation <span XXXXX="ql-XXXXXXX" XXXX-value="\sigma"><span class="katex"><span class="XXXXX-mathml"></span><span XXXXX="katex-html"><span class="base"><span class="strut"></span><span class="mord mathdefault">σ</span></span></span></span></span> = <span XXXXX="ql-XXXXXXX" XXXX-value="\XXXX{XXX}"><span class="katex"><span class="XXXXX-XXXXXX"></span><span XXXXX="katex-XXXX"><span class="base"><span class="XXXXX"></span><span XXXXX="mord sqrt"><span class="vlist-t XXXXX-t2"><span class="XXXXX-r"><span class="vlist"><span class="svg-align"><span XXXXX="XXXXXX"></span><span class="XXXX"><span XXXXX="mord mathdefault">n</span><span class="XXXX mathdefault">p</span><span XXXXX="XXXX mathdefault">q</span></span></span><span XXXXX="pstrut"></span><span class="XXXX-XXXX"></span></span></span></span></span></span></span></span></span></p> <p><span XXXXX="XXXXX-s"></span><span class="XXXXX-r"><span XXXXX="XXXXX"></span></span> =<span XXXXX="ql-XXXXXXX" XXXX-XXXXX="\sqrt{20/3}"><span class="katex"><span XXXXX="XXXXX-XXXXXX"></span><span XXXXX="XXXXX-XXXX"><span XXXXX="XXXX"><span class="XXXXX"></span><span XXXXX="mord sqrt"><span class="XXXXX-t vlist-t2"><span class="XXXXX-r"><span class="vlist"><span XXXXX="XXX-align"><span class="pstrut"></span><span class="XXXX"><span class="mord">X</span><span class="mord">X</span><span class="mord">/</span><span class="mord">3</span></span></span><span XXXXX="XXXXXX"></span><span XXXXX="XXXX-XXXX"></span></span></span></span></span></span></span></span></span></p> <p><span XXXXX="XXXXX-s"></span><span class="vlist-r"><span class="vlist"></span></span> =X.XX</p> <p>P(<span XXXXX="XX-XXXXXXX" XXXX-value="\bar{X}"><span XXXXX="katex"><span XXXXX="XXXXX-XXXXXX"></span><span XXXXX="XXXXX-XXXX"><span XXXXX="XXXX"><span class="XXXXX"></span><span XXXXX="XXXX accent"><span XXXXX="XXXXX-t"><span class="XXXXX-r"><span class="XXXXX"><span class="XXXXXX"></span><span class="mord"><span class="XXXX mathdefault">X</span></span><span XXXXX="pstrut"></span><span class="accent-body">X</span></span></span></span></span></span></span></span></span>≥8)=1-X(<span class="ql-formula" XXXX-value="\bar{X}"><span class="XXXXX"><span XXXXX="katex-XXXXXX"></span><span class="katex-XXXX"><span class="XXXX"><span XXXXX="strut"></span><span class="XXXX XXXXXX"><span XXXXX="XXXXX-t"><span XXXXX="vlist-r"><span class="vlist"><span XXXXX="pstrut"></span><span class="mord"><span class="mord XXXXXXXXXXX">X</span></span><span XXXXX="pstrut"></span><span XXXXX="accent-body">X</span></span></span></span></span></span></span></span></span> < X)=1-<span class="XX-XXXXXXX" XXXX-value="\Phi"><span class="katex"><span class="katex-mathml"></span><span class="XXXXX-html"><span XXXXX="base"><span class="strut"></span><span XXXXX="XXXX">Φ</span></span></span></span></span> [(X-10)/(X.XX/<span class="XX-XXXXXXX" data-XXXXX="\sqrt{XX}"><span class="XXXXX"><span class="katex-mathml"></span><span XXXXX="XXXXX-html"><span class="base"><span class="strut"></span><span class="XXXX XXXX"><span class="vlist-t XXXXX-XX"><span class="XXXXX-r"><span XXXXX="vlist"><span class="svg-XXXXX"><span class="XXXXXX"></span><span class="mord"><span class="XXXX">3</span><span XXXXX="mord">X</span></span></span><span XXXXX="pstrut"></span><span XXXXX="hide-XXXX"></span></span></span></span></span></span></span></span></span></p> <p><span XXXXX="XXXXX-s"></span><span class="XXXXX-r"><span class="XXXXX"></span></span> )] =X-<span class="ql-formula" data-XXXXX="\XXX"><span XXXXX="XXXXX"><span class="XXXXX-mathml"></span><span class="XXXXX-html"><span XXXXX="base"><span class="XXXXX"></span><span XXXXX="XXXX">X</span></span></span></span></span> (-2/X.471)=1-<span class="ql-XXXXXXX" data-value="\XXX"><span XXXXX="XXXXX"><span class="XXXXX-mathml"></span><span class="katex-XXXX"><span XXXXX="XXXX"><span class="XXXXX"></span><span XXXXX="mord">X</span></span></span></span></span> (-4.XX) =1- [X-<span class="ql-XXXXXXX" data-value="\XXX"><span XXXXX="XXXXX"><span XXXXX="katex-XXXXXX"></span><span class="katex-XXXX"><span class="base"><span class="strut"></span><span class="mord">Φ</span></span></span></span></span> (4.24)] =X-1+1 =1</p><p></p>">
