At the movies: A movie theater is considering a showing of Puppet Master for a $80\text{'}$s thowback night. In

order to ensure the success of the evening, they've asked a random sample of $85$ patrons whether they

would come to the showing or not. Of the $85$ patrons, $27$ said that they would come to see the film.

Construct a $95\%$ confidence interval to determine the true proportion of all patrons who would be

interested in attending the showing.

a$)$ What is the point estimate for the true proportion of interested patrons? $($please input a proportion

accurate to four decimal places$)$

b$)$ Complete the interpretation of the confidence interval. Please provide the bounds for the confidence

interval in decimal form, accurate to four decimal places, and list the lower bound first.

$"$We are

$\%$ confident that the true proportion of patrons interested in attending the

showing of Puppet Master is between

and

$."$

c$)$ The theater is only willing to show Puppet Master if they are confident that at least $40\%$ of their patrons

would be interested in seeing the film. Should they show it$?$