A programmer plans to develop a new software system. In planning for the operating system that he will​ 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 99​% confident that his estimate is in error by no more than two percentage points question mark s?​a) Assume that nothing is known about the percentage of computers with new operating systems. n=.(Round up to the nearest​ integer.)b) Assume that a recent survey suggests that about 96​% of computers use a new operating system. n=.(Round up to the nearest​ integer.)

a)  

And rounded up we have that n=4161

b)  

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 and . And the critical value would be given by:

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

   (a)  

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

  (b)  

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

And rounded up we have that n=4161

Part b

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

And replacing we got:

And rounded up we have that n=640

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step-by-step explanation: