Answer:
A sample of 11352 is needed.
Step-by-step explanation:
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 zscore that has a pvalue of .
The margin of error is given by:
For this problem, we have that:
400 cards, 120 cases were correct. So
95% confidence level
So , z is the value of Z that has a pvalue of , so .
How large a sample n would you need to estimate p with margin of error 0.01 and 95% confidence
We would need a sample of size n, and n is found when . So
Rounding up
A sample of 11352 is needed.