When it says slighty may vary, my calculations were off with this one. thank you for providing a step by step with this.

a) let p represent i got 382.8

b) for upper limit i got 30.2

lower limit i got 29.9

i picked : We are 5% confident that the true proportion of actors who are extroverts falls above this interval.

c) i picked : No, the conditions are not satisfied. This is important because it allows us to say that p is approximately binomial.

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a random sample of 62 professional actors, it was found that 43 were extroverts. (a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.)

_________

(b)

Find a 95% confidence interval for p. (Round your answers to two decimal places.)

lower limit_____

upper limit_____

Give a brief interpretation of the meaning of the confidence interval you have found.

• We are 5% confident that the true proportion of actors who are extroverts falls within this interval.

• We are 5% confident that the true proportion of actors who are extroverts falls above this interval.

• We are 95% confident that the true proportion of actors who are extroverts falls within this interval.

• We are 95% confident that the true proportion of actors who are extroverts falls outside this interval.

(c)

Do you think the conditions np> 5 and nq> 5 are satisfied in this problem? Explain why this would be an important consideration.

• Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately normal.

• No, the conditions are not satisfied. This is important because it allows us to say that p is approximately normal.

• Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately binomial.

• No, the conditions are not satisfied. This is important because it allows us to say that p is approximately binomial.