Question

how do i plug this in my 81 t4 calculator can you explain it to me in simple ways having trouble please . i have a test on these .

Answer 1

Solution :

( a )

$\mathrm{Given\::}$

$\mu =69$

$\sigma =2.8$

$z=\frac{x-\mu }{\sigma }=\frac{72-69}{2.8}=\frac{3}{2.8}=1.07143\approx 1.07$

$\mathrm{Probability\:that\:he\:can\:fit\:through\:thedoorway\:without\:bending}$

$\mathrm{P}(x<72)=\mathrm{P}(z<1.07)=0.85769\approx 0.8577$

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( b )

$\mathrm{Given\::}$

$\mu =69$

$\sigma =2.8$

$n=100$

$z=\frac{x-\mu }{\frac{\sigma}{\sqrt{n}} }=\frac{72-69}{\frac{2.8}{\sqrt{100}}}$

$=\frac{3}{\frac{2.8}{\sqrt{100}}}$

$=\frac{3\sqrt{100}}{2.8}$

$=\frac{3*10}{2.8}$

$=\frac{30}{2.8}$

$=10.71429\approx 10.71$

$=10.71$

$\mathrm{The\:cumulative\:area\:is\:0.9999}$

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( c )

$\mathrm{C.\quad\:The\:probability\:from\:part\:(a)\:is\:more\:relevant\:because\:it\:shows\:the\:proportion\:of\:male\:passengers\:}$$\mathrm{that\:will\:not\:need\:to\:blend.}$

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( d )

$\mathrm{B.\quad\:Since\:men\:are\:generally\:taller \:than\:women,\:a\:design\:that\:accommodates\:a\:suitable\:proportion\:of\:men}$$\mathrm{will\:necessarily\:accommodate\:a \:greater\:proportion\:of\:women.}$