Donald claims that Billa is the cutest dog in the world. Slightly more circumspect, Mike allows that Billa is “one in a million.” Seizing the opportunity to revel in Billa’s charm, Donald devises a procedure for measuring CCQ (canine cuteness quotient), which she calibrates so that CCQ ∼ Normal(50, 450). Assuming that Mike is correct, what is Billa’s CCQ score?
normal deviation and standard deviation
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$\begingroup$
probability
statistics
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0You mean that the mean is $50$ and the standard deviation is $450$? – 2017-02-11
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0@lulu : I would take it to mean the variance is $450$, so the standard deviation is $\sqrt{450} = 15\sqrt2.$ That the s.d. would be such a huge number as $450$ defies common sense. – 2017-02-12
1 Answers
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$$\Pr(Z> c) = 0.000001 = \frac 1 {\text{1 million}} $$
The number $c$ you can get from your software or from a table of the kind found in the back of every textbook.
$$ \Pr\left( \frac{\text{CCQ} - 50}{\sqrt{450}} > c \right) = 0.000001 $$ Plug in the number $c$ that you got from the table. Then solve the equation $\dfrac{\text{CCQ} - 50}{\sqrt{450}}=c $ for $\text{CCQ}.$
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0use pnorm or qnorm? – 2017-02-11
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0@user410961 : Try it and see. – 2017-02-11
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0In R, `qnorm` is the quantile function (inverse CDF): `qnorm(1-10^-6, 50, sqrt(450))` returns 150.8354. Also, `pnorm` is the CDF: `1-pnorm(150, 50, sqrt(450))` returns 1.214234e-06. You can fuss with it. – 2017-02-12