How hot is the air in the top (crown) of a hot air balloon? Information from Ballooning: The Complete Guide to Riding the Winds, by Wirth and Young (Random House), claims that the air in the crown should be an average of 100C for a balloon to be in a state of equilibrium. However, the temperature does not need to be exactly 100C. This range may vary with the size and (decorative) shape of the balloon. All balloons have a temperature gauge in the crown. Suppose that 54 readings (for a balloon in equilibrium) gave a mean temperature of x = 97C. For this balloon, 16C. Find a 95% confidence interval for the mean temperature (in degrees Celsius) in the crown of this balloon when it's in equilibrium. (Enter your answer in the form: lower limit to upper limit. Include the word "to." Round your numerical values to two decimal places.)

In a random sample of66professional actors, it was found that45were extroverts.(a)Letprepresent the proportion of all actors who are extroverts. Find a point estimate forp. (Round your answer to four decimal places.)

(b)Find a 95% confidence interval forp. (Enter your answer in the form: lower limit to upper limit. Include the word "to." Round your numerical values to two decimal places.)

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

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

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

We are 5% 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 within this interval.

(c)Do you think the conditionsnp>5 andnq>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 thatpis approximately normal.

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

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

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