Mathematics, 03.06.2020 13:15 sanchezhailey4702

A programmer plans to develop a new software system. In planning for the operating system that he willâ€‹ use, he needs to estimate the percentage of computers that use a new operating system. How many computers must be surveyed in order to be 99â€‹% confident that his estimate is in error by no more than two percentage points question mark s?â€‹a) Assume that nothing is known about the percentage of computers with new operating systems. n=.(Round up to the nearestâ€‹ integer.)b) Assume that a recent survey suggests that about 96â€‹% of computers use a new operating system. n=.(Round up to the nearestâ€‹ integer.)

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Answer from: jessixa897192

a) $n=\frac{0.5(1-0.5)}{(\frac{0.02}{2.58})^2}=4160.25$

And rounded up we have that n=4161

b) $n=\frac{0.96(1-0.96)}{(\frac{0.02}{2.58})^2}=639.01$

And rounded up we have that n=640

Step-by-step explanation:

Part a

The confidence level is 99% , our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58$

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 $ME =\pm 0.02$ 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)

Since we don't have prior info for the true proportion we can use $\hat p=0.5$ . And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.02}{2.58})^2}=4160.25$

And rounded up we have that n=4161

Part b

For this case we have a prior estimation ofr the proportion:

$\hat p=0.96$

And replacing we got:

$n=\frac{0.96(1-0.96)}{(\frac{0.02}{2.58})^2}=639.01$

And rounded up we have that n=640

Answer from: Quest

points are handed out whenever you post answers.

brainliest answers are handed out by the person asking the question, so whether your answer is picked depends entirely on whether the asker bothers to pick

if you're asking about your rank, it depends on having a certain number of points and a certain number of brainliest answers. for example, at the time of this writing, i have 44338 points out of 15000 needed for the next (nearly triple the requirement! ) but i only have 24 out of 50 required brainliest answers. this number decays, meaning after a certain amount of time (i think about a month), the total number of brainliest answers you've earned doesn't count toward this total. (i've been stuck at the same rank for a long

the lesson to learn here is that you shouldn't worry about points or rank. chances are, no matter how good an answer you may provide, your efforts will go mostly unnoticed unless you focus on the newest/most active questions that get posted.

Answer from: Quest

Jim has run 5/6 of a mile so far. i hope that answers your question! good luck : )

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A programmer plans to develop a new software system. In planning for the operating system that he wi...