(Solved): or this problern, carry at least four digits after the decamal in your calculations. Arcowers may v ...

or this problern, carry at least four digits after the decamal in your calculations. Arcowers may vary shightly due to rounding- a random samples of tre professional actors, it wars found that 37 were extroverts. (b) find a 95\%i confidence interval for \( p \). (foound your answers to two decirnal placess) lower lirsit: upper liernt Give a bief interpectation of the meaning of the confudence interval you hive found. We ate \( 5 \% \) confident that the true proportion of acturs who are exveverts falls above this interval. Wh are \( 5 \% \) confolent that the true proportion of actors who are extroverts falls within this interval, We are \( 95 \% \) conident that the true proportion of actors who are extroverts falls witin this interval. We are \( 45 \% \) contident that the true properticin of actors who are antronerts falls ouriade this interval. (c) Do you think the conditions \( m p>5 \) and \( \cap-q>5 \) are satisfied in this protelem? Explain why this would be an irnportant cansideration, No, the contitions igre not satisfied. This as impartant because it allows us to suy that f is approximately bincmiati No, the conditions are not satisfied. This is impartant because it allows us to say that p is spereximatety nonmal: Yes, the conditions are satisfied. This is important because it allows us to say that \( \beta \) is approximately nermal. Yes, the condsions are satisherf. This is important because it allows us to say that \( \beta \) is approximately binemial.