tiffanydowell13

08.12.2020 •

Mathematics

Y
-2
2
X
What is y= x+

Solved

Show answers

Ответ:

KayJahnae04

12.03.2023

Mathematics

a) We are interested on this probability

P(X13.17)

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:

$P(X13.17)=P(\frac{X-\mu}{\sigma}\frac{13.17-\mu}{\sigma})=P(Z\frac{13.17-13}{0.5})=P(z0.34)=0.367$

b) $P(\bar X 13.17)$

The new z score is given by:

$z =\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And replacing we got:

$P(\bar X 13.17)=P(Z \frac{13.17-13}{\frac{0.5}{\sqrt{36}}})= P(Z2.04) =0.0207$

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".

Part a

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:

$X \sim N(13,0.5)$

Where $\mu=13$ and $\sigma=0.5$

We are interested on this probability

P(X13.17)

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:

$P(X13.17)=P(\frac{X-\mu}{\sigma}\frac{13.17-\mu}{\sigma})=P(Z\frac{13.17-13}{0.5})=P(z0.34)=0.367$

Part b

Since the distribution for X is normal then we can conclude that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And we want this probability:

$P(\bar X 13.17)$

The new z score is given by:

$z =\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And replacing we got:

$P(\bar X 13.17)=P(Z \frac{13.17-13}{\frac{0.5}{\sqrt{36}}})= P(Z2.04) =0.0207$

0,0(0 оценок)

Ask your question to the AI advisor

Ai-bot is an expert in any field and is the perfect companion for reliable and useful answers and advice on a variety of topics, including science, history, technology, art, sports, health, culture and more.

Ask your question

More tips

Answers on questions: Mathematics

Ask an AI advisor a question

I want advice

Y -2 2 X What is y= x+