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 90% confident that his estimate is in error by no more than one percentage point?

a. Assume that nothing is known about the percentage of computers with new operating systems. n = ?
b. Assume that a recent survey suggests that 99% of computers use a new operating system. n = ?

a)

b) n = 381

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

The margin of error is:

90% confidence level

So , z is the value of Z that has a pvalue of , so .

a. Assume that nothing is known about the percentage of computers with new operating systems. n = ?

When we do not know the proportion, we use , which is when we are going to need the largest sample size.

The sample size is n when M = 0.01.

b. Assume that a recent survey suggests that 99% of computers use a new operating system. n = ?

Now we have that . So

Rouding up

n = 381

d 192

step-by-step explanation:

we find our area to find area we multiply thoses numbers to get our answer so our area is 192

the radius is 2 times the diameter.

step-by-step explanation: