A math teacher is investigating the problem of students losing their graphing calculators because their names aren’t written on them. In a random sample of 50 students, only 32 had their names written on their graphing calculators. The teacher constructs a 99% confidence interval for the proportion of all students at this school who have their names written on their graphing calculators and obtains (0.465, 0.815). What is the correct interpretation of this confidence interval? The teacher can be 99% confident that a majority of students at this school write their names on their graphing calculators.

The teacher can be 99% confident that the interval from 46.5% to 81.5% captures the true proportion of students who write their names on their graphing calculators.

In 99% of samples taken, between 46.5% and 81.5% of the sampled students would write their names on their graphing calculators.

There is a 1% probability that the proportion of all students who write their names on their graphing calculators is either below 0.465 or above 0.815.