# 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 be90​%confident that his estimate is in error by no more thanfivepercentagepoints question marks?Complete parts​ (a) through​ (c) below.​a) Assume that nothing is known about the percentage of computers with new operating systems.

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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
five
percentage
points question marks?
Complete parts​ (a) through​ (c) below.
​a) Assume that nothing is known about the percentage of computers with new operating systems.
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Step 1

Introduction:

The 100 (1 – α) % confidence interval for the population proportion, π is: (π – (/2­) (π (1 – π)/n), π + (/2­) (π (1 – π)/n)).

Here, n is the sample size, p is the sample proportion, and /2 is the critical value of the z-distribution, above which, 100 (α/2) % or α/2 proportion of the observations lie.

The quantity, (/2&sh...

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