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3 years ago

Select the equation written in standard form.

Mathematics

1 answer:

Elden [556K]3 years ago

5 0

Answer:

Step-by-step explanation:

standard form is y=mx+b

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$P(X>3.75)=P(\frac{X-\mu}{\sigma}>\frac{3.75-\mu}{\sigma})=P(Z>\frac{3.75-4}{0.5})=P(z>-0.5)$

And we can find this probability using the complement rule and we got:

$P(z>-0.5)=1-P(z$

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 weights of a population, and for this case we know the distribution for X is given by:

$X \sim N(4,\sqrt{0.25}=0.5)$

Where $\mu=4$ and $\sigma=0.5$

We are interested on this probability

$P(X>3.75)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>3.75)=P(\frac{X-\mu}{\sigma}>\frac{3.75-\mu}{\sigma})=P(Z>\frac{3.75-4}{0.5})=P(z>-0.5)$

And we can find this probability using the complement rule and we got:

$P(z>-0.5)=1-P(z$

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