<img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B25%20%5Ctimes%209%29x%7D%20" id="TexFormula1" title=" \sqrt{25 \times 9)x} " alt=

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Ira Lisetskai [31]

3 years ago

" \sqrt{25 \times 9)x} " align="absmiddle" class="latex-formula">

Mathematics

1 answer:

Daniel [21]3 years ago

4 0

Answer:

$15\sqrt{x}$

Step-by-step explanation:

$\sqrt{(25*9)x}$

Start by "taking out" the perfect squares. 25 and 9 are perfect squares (and pretty common ones).

The square root of 25 is 5 and the square root of 9 is 3. Therefore you can take out a 5 and 3 from the radical. Multiply the numbers you take out together.

5 * 3 = 15

The number outside of the radical sign will be a 15, and x is left over inside the radical. The final answer is $15\sqrt{x}$ .

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We can use the z score formula given by:

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If we use this formula we got:

$z=\frac{21-20}{\frac{9.31}{\sqrt{18}}}= 0.456$

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And using a calculator, excel or the normal standard table and we have that:

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Step-by-step explanation:

We assume this previous info: It is known that the amounts of time required for room-service delivery at a certain Marriott Hotel are Normally distributed with the average delivery time of 20 minutes.

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

$X \sim N(20,9.31)$

Where $\mu=20$ and $\sigma=9.31$

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

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

And we can use the z score formula given by:

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

If we use this formula we got:

$z=\frac{21-20}{\frac{9.31}{\sqrt{18}}}= 0.456$

$z=\frac{25-20}{\frac{9.31}{\sqrt{18}}}= 2.279$

And using a calculator, excel or the normal standard table and we have that:

$P(0.456$

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