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3 years ago

Multiply and simplify.

Mathematics

1 answer:

GuDViN [60]3 years ago

3 0

Answer:

6x³ + x² - 9x +10

Step-by-step explanation:

This one uses typical FOIL multiplication.

We are given the expression (3x + 5) (2 $x^{2}$ – 3x + 2)

Using FOIL, we multiply every term in all ways. We can rewrite the expression as (3x · 2 $x^{2}$ ) + (3x · -3x) + (3x · 2) + (5 · 2 $x^{2}$ ) + (5 · -3x) + (5 · 2)

Which simplifies to 6x³ - 9x² + 6x + 10x²- 15x + 10

Which we can further simplify to 6x³ + x² - 9x +10

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Answer:

$X \sim N(61,14)$

Where $\mu=61$ and $\sigma=14$

Since the distribution for X is normal then the distribution for the sample mean is also normal and given by:

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

$\mu_{\bar X} = 61$

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So then is appropiate use the normal distribution to find the probabilities for $\bar X$

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". The letter $\phi(b)$ is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: $\phi(b)=P(z$

Solution to the problem

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

$X \sim N(61,14)$

Where $\mu=61$ and $\sigma=14$

Since the distribution for X is normal then the distribution for the sample mean $\bar X$ is also normal and given by:

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

$\mu_{\bar X} = 61$

$\sigma_{\bar X}= \frac{14}{\sqrt{6}}= 5.715$

So then is appropiate use the normal distribution to find the probabilities for $\bar X$

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