In a certain state in the USA, “irreconcilable differences” is given as the legal reason in 80% of all
divorce cases. Find the probability that in the next 30 divorce cases filed in this state,
(a) at least 28 will claim “irreconcilable differences” as the reason.
(b) exactly 19 will claim “irreconcilable differences” as the reason.
(c) Find the mean and variance of the number of divorce cases that cite “irreconcilable
differences” as the reason for divorce.
In A Certain State In The Usa Irreconcilable Differences Is Given As The Legal Reason In 80 Of All Divorce Cases Fi 1 (57.75 KiB) Viewed 29 times
In A Certain State In The Usa Irreconcilable Differences Is Given As The Legal Reason In 80 Of All Divorce Cases Fi 2 (57.75 KiB) Viewed 29 times
1 In a certain state in the USA, "irreconcilable differences is given as the legal reason in 80% of all divorce cases. Find the probability that in the next 30 divorce cases filed in this state, (a) at least 28 will claim irreconcilable differences as the reason (b) exactly 19 will claim irreconcilable differences as the reason (c) Find the mean and variance of the number of divorce cases that cite "irreconcilable differences as the reason for divorce. (10 points) Two tourists are enjoying the view from San Francisco's Golden Gate Bridge. They have decided to spend some time waiting for ships to pass under the bridge Suppose that ship arrivals at the & 2 3. a Golden Gate (leaving or entering San Francisco Bay) are a Poisson distribution at a mean rate of 2 *0.4 per hour. (a) What is the probability that the tourists will see 1 to 3 ships passing beneath them if they spend 1 hour waiting for the ships? (b) What is the probability that the tourists will see at most 2 ships passing beneath them it they spend 30 minutes waiting for the ships? (c) What is the probability that the tourists will see at least 3 ships passing beneath them if they spend 2 hours waiting for the ships? [10 points) At a certain casino, there is a gambling same where balls of equal weights are numbered from 1 to 15, placed inside a tambiolo, and mixed up. Three balls are selected at random without replacement, one after the other in succession (a) A certain casino patron, Mr. Lee has enough money only to play a total of 4 bets for the night. Mr. Lee always bets that the outcome will be such that among the 3 balls selected, the lowest number is a number lower than "6". After a streak of bad luck, what is the probability that Mr. Lee will finally be lucky and win on the bet? (b) Another casino patron, Mr. Lewis has enough money to keep playing the game until he has won 7 bets. If Mr. Lewis always bets that the outcome will be such that among the 3 balls selected, there are no consecutive numbers, what is the probability that he places a total of at most 12 bets? (c) Another casino patron, Ms. Lane has enough money to keep playing the game until she has won S bets. If Ms. Lane bets that the outcome will be such that exactly two of the three numbered balls are perfect squares, what is the probability she places at least 10 bets? [10 points) Jack and fill are playing a game of bowing Suppose that both are seasoned players, and that Jack's bowling score is normally distributed with a mean of 170 and a standard deviation 8 whereas sil's bowling score is normally distributed with a mean of 175 and standard deviation of 10. Find the probability that (a) at least one of the scores over 180 in a game. (b) both Jack & Jil score somewhere between 168 to 172. [8 points) (This port does not require a computer solution) Find the value of the constante so that the following function is the probability density function of the random variable X that is normally distributed. Identify the mean and variance of f(x) = ce- 2-2-c<x< (This part requires a computer solution) in addition, find the probability P(0.9 <x< 1.1) 17 points) 4. 5.
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