How many adults must you survey in order to be 96 confident

How many adults must you survey in order to be 96% confident that your estimate is within 5% of the tru population percentage, if nothing is known about the population percentage.

Solution

Sample size is required for a survey for 96% confidence interval

margin of error = 5% = 0.05

Population percentage = unknown

Margin of error for 96% = 2.05 ( std error)

Let us assume that population std dev =1

Then 2.05 (1/rtn) < 0.05

rtn >2.05/0.05

n>1681