Question

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

Answer 1

Solution :

Given that,

(a)

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 5% = 0.05

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (2.576 / 0.05)² * 0.5 * 0.5

= 663.6

sample size = 664

664 computers must be surveyed .