The 2010 General Social Survey reported a sample where about 48% of US residents thought marijuana should be made legal. If we wanted to limit the margin of error of a 95% confidence interval to 4%, about how many Americans would we need to survey

The sample size is  

Step-by-step explanation:

From the question we are told that

    The  sample proportion is  

     The  margin of error is  

Given that the confidence level is 95%  the level of significance is mathematically represented as

Next  we obtain the critical value of   from the normal distribution table , the values is

The reason we are obtaining critical value of     instead of     is because  

represents the area under the normal curve where the confidence level interval (  ) did not cover which include both the left and right tail while  

is just the area of one tail which what we required to calculate the margin of error

Generally the margin of error is mathematically represented as

substituting values

=>      

step-by-step explanation:

try remembering the steps