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3 years ago

Explain how to make these couculations mentaly a. 99+54 b.244-99

Mathematics

1 answer:

IrinaVladis [17]3 years ago

5 0

<h2><u>PLEASE MARK BRAINLIEST!</u></h2>

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Answer:

Use estimation

Step-by-step explanation:

A) 99 + 54

estimate that 99 is 100

estimate that 54 is 55

Add 100 and 55 together

100 + 55 = 155

Remember that you added 1 to 99 and 1 to 55

So you must subtract 2 from 155

155 - 2 = 153

Your answer is 153.

B) 244 - 99

estimate that 244 is 245

estimate that 99 is 100

Add 245 and 100 together

245 + 100 = 345

Remember that you added 1 to 245 and 1 to 99

So you must subtract 2 from 345

345 - 2 = 343

Your answer is 343.

<em>Remember that you are doing all of this in your head!</em>

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I hope this helps!

- sincerelynini

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Marizza181 [45]

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.04}{1.64})^2}=420.25$

And rounded up we have that n=421

Step-by-step explanation:

We know that the sample proportion have the following distribution:

$\hat p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.04$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We assume that a prior estimation for p would be $\hat p =0.5$ since we don't have any other info provided. And replacing into equation (b) the values from part a we got: