2.

Mathematics

1 answer:

Gekata [30.6K]1 year ago

7 0

Answer: the system has no solution.

Step-by-step explanation:

\displaystyle\\

\left \{ {{x^2y=16\ \ \ \ \ (1)} \atop {x^2+4y+16=0\ \ \ \ \ (2)}} \right. .\\

Multiply\ both\ sides\ of\ the\ equation\ (2)\ by\ y\ (y\neq 0):\\

x^2y+4y^2+16y=0\\

We\ substitute\ equation\ (1)\ into\ equation\ (2):\\

16+4y^2+16y=0\\

4y^2+16y+16=0\\

4*(y^2+4y+4)=0\\

4*(y^2+2*y*2+2^2)=0\\

4*(y+2)^2=0\\

Divide\ both\ sides\ of\ the \ equation\ by\ 4:\\

(y+2)^2=0\\

(y+2)*(y+2)=0\\

So,\ y+2=0\\

y=-2.\\

$\displaystyle\\We\ substitute\ the\ value\ of\ y\ into\ equation\ (1):\\x^2*(-2)=16\\Divide\ both\ sides\ of\ the \ equation\ by\ -2:\\x^2=-8\\x^2\geq 0\\ Hence,\ the\ system\ has\ no\ solution.$

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If outliers are discarded, then the retirement savings by residents of Econistan is normally distributed with a mean of $100,000

zavuch27 [327]

Answer:

$P(X>117000)=P(\frac{X-\mu}{\sigma}>\frac{117000-\mu}{\sigma})=P(Z>\frac{117000-100000}{20000})=P(z>0.85)$

And we can find this probability using the complement rule and the normal standard table or excel:

$P(z>0.85)=1-P(z$

The firgure attached illustrate the problem

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the retirement savings of a population, and for this case we know the distribution for X is given by:

$X \sim N(100000,20000)$