- 4 Suppose You Play A Game Of Chance In Which You Roll Two Fair Dice You Pay 2 To Enter The Game You Win 10 If You 1 (171.03 KiB) Viewed 110 times
4. Suppose you play a game of chance; in which you roll two fair dice. You pay $2 to enter the game. You win $10 if you get all two dice with an even number of dots on the top face. Otherwise, you win nothing. (In any case, you don't get your $2 back). (Hint: Use sample Space table to determine outcomes) (10 points) a. Over the long term, what is your expected profit of playing the game? (6 points) (hint: Use probability distribution table) b. If you played this game 100 times, how much would you expected to win/ lose? C. 5. 66% of Americans support death penalty (Gallup, 2004). Five people are randomly selected. Let the random variable X be the number of Americans that support death penalty. (10 points) a. Explain why X is a binomial random variable. b. What is the probability that exactly 4 people selected support death penalty? (4 points) (2 points) c. What is the probability that at least 2 people selected are against death penalty (4 points) 6. The lengths of pregnancies of orca whales are normally distributed with mean of 505 days and a standard deviation of 18 days. (10 points) a. What percentage of orca pregnancies last 535 days or longer? b. If we stipulate that a newborn orca is premature if the length of pregnancy is in the lowest 4%, find the length (gestation) that separates premature babies from those who are not premature. (5 points) (10 points) 7. A sample of 35 teens aged 15-18 years showed an average of 2.9 hours of cell phone use per day with a standard deviation of 0.5 hours. (15 points) a. Find a 90% confidence interval for a number of hours per day teens in this age group spend using cell phone. (10 points). b. If you increase the confidence level, will the confidence interval estimate be wider or (5 points) narrower? Explain.