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Question Number 200792 by sonukgindia last updated on 23/Nov/23

Commented by Frix last updated on 23/Nov/23

Do you know the answer? Is it 63.77%?

$$\mathrm{Do}\:\mathrm{you}\:\mathrm{know}\:\mathrm{the}\:\mathrm{answer}? \\ $$$$\mathrm{Is}\:\mathrm{it}\:\mathrm{63}.\mathrm{77\%}? \\ $$

Commented by sonukgindia last updated on 23/Nov/23

how?

$${how}? \\ $$

Commented by Frix last updated on 23/Nov/23

I think μ=32.66×36=1175.76 σ=1.36×36=48.96 x=1193 z=((x−μ)/σ)≈.352328 (1/( (√(2π))))∫_(−∞) ^z e^(−(x^2 /2)) dx≈.637704

$$\mathrm{I}\:\mathrm{think} \\ $$$$\mu=\mathrm{32}.\mathrm{66}×\mathrm{36}=\mathrm{1175}.\mathrm{76} \\ $$$$\sigma=\mathrm{1}.\mathrm{36}×\mathrm{36}=\mathrm{48}.\mathrm{96} \\ $$$${x}=\mathrm{1193} \\ $$$${z}=\frac{{x}−\mu}{\sigma}\approx.\mathrm{352328} \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}\pi}}\underset{−\infty} {\overset{{z}} {\int}}\mathrm{e}^{−\frac{{x}^{\mathrm{2}} }{\mathrm{2}}} {dx}\approx.\mathrm{637704} \\ $$

Commented by mr W last updated on 23/Nov/23

i think it′s correct.

$${i}\:{think}\:{it}'{s}\:{correct}. \\ $$

Answered by mr W last updated on 23/Nov/23

((1399)/(36))=33.14 ((x−μ)/( σ(√2)))=((33.14−32.66)/(1.36×(√2)))=0.24957 (1/2)[1+erf(((x−μ)/(σ(√2))))]≈63.79%

$$\frac{\mathrm{1399}}{\mathrm{36}}=\mathrm{33}.\mathrm{14} \\ $$$$\frac{{x}−\mu}{\:\sigma\sqrt{\mathrm{2}}}=\frac{\mathrm{33}.\mathrm{14}−\mathrm{32}.\mathrm{66}}{\mathrm{1}.\mathrm{36}×\sqrt{\mathrm{2}}}=\mathrm{0}.\mathrm{24957} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\left[\mathrm{1}+{erf}\left(\frac{{x}−\mu}{\sigma\sqrt{\mathrm{2}}}\right)\right]\approx\mathrm{63}.\mathrm{79\%} \\ $$

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