The fox tv network is considering replacing one of its prime-time crime investigation shows with a new family-oriented comedy show. before a final decision is made, network executives designed an experiment to estimate the proportion of their viewers who would prefer the comedy show over the crime investigation show. a random sample of 400 viewers was selected and asked to watch the new comedy show and the crime investigation show. after viewing the shows, 250 indicated they would watch the new comedy show and suggested it replace the crime investigation show. (round your answers to 3 decimal places.)

a. estimate the value of the population proportion.

b. determine the 99% confidence interval for the population proportion.

John and daphne are saving for their daughter ellen's college education. ellen just turned 10 at (t = 0), and she will be entering college 8 years from now (at t = 8). college tuition and expenses at state u. are currently $14,500 a year, but they are expected to increase at a rate of 3.5% a year. ellen should graduate in 4 years--if she takes longer or wants to go to graduate school, she will be on her own. tuition and other costs will be due at the beginning of each school year (at t = 8, 9, 10, and 11).so far, john and daphne have accumulated $15,000 in their college savings account (at t = 0). their long-run financial plan is to add an additional $5,000 in each of the next 4 years (at t = 1, 2, 3, and 4). then they plan to make 3 equal annual contributions in each of the following years, t = 5, 6, and 7. they expect their investment account to earn 9%. how large must the annual payments at t = 5, 6, and 7 be to cover ellen's anticipated college costs? a. $1,965.21b. $2,068.64c. $2,177.51d. $2,292.12e. $2,412.76