A recent poll surveyed $52,480$ adults about their exercise habits. Out of those surveyed, $18,412$ reported that they exercise at least $3$ times per week. Construct a $95\%$ confidence interval for the true proportion of adults who exercise at least $3$ times per week. Interpret the result.

We are $95\%$ confident that the true proportion of all adults who exercise at least $3$ times per week lies between $34.7\%$ and $35.5\%$

There is a $95\%$ probability that the true proportion of all adults who exercise at least $3$ times per week lies between $34.7\%$ and $35.5\%$

We are $95\%$ confident that the true proportion of all adults who exercise at least $3$ times per week lies between $45.7\%$ and $46.8\%$

There is a $95\%$ probability that the true proportion of all adults who exercise at least $3$ times per week lies between $45.7\%$ and $46.8\%$