1) A school has 1600 students and they are going to vote as to whether they will completely convert the school completely off fossil fuels. How many students would you have to poll to be 95% confident of the outcome within /- 2% of the vote

Using the z-distribution, it is found that you would have to poll 2401 students.

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 z-score that has a p-value of .

The margin of error is:

95% confidence level, hence, z is the value of Z that has a p-value of , so .

There is no prior estimate, hence is used.

The sample size is n for which M = 0.02, hence:

You would have to poll 2401 students.

To learn more about the z-distribution, you can take a look at link

Standard deviation of the students = 0.408

The students would you have to poll to be 95% confident of the outcome within /- 2% of the vote  

         = 0.408 X 1600

         = 652.8    

Step-by-step explanation:  

Step(i):-

Given sample size 'n' = 1600

95% confidence interval of the margin error is determined by

Level of significance = 0.05

Z₀.₀₅ = 1.96

Given Margin of error = 2% = 0.02

      0.02 X √1600 = 1.96 X S.D

Standard deviation of the students = 0.408

The students would you have to poll to be 95% confident of the outcome within /- 2% of the vote  

         = 0.408 X 1600

         = 652.8  

sine

step-by-step explanation: