Statistics

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International Pictures is trying to decide how to distribute its new movie ‘Claws’. ‘Claws’ is the story of an animal husbandry experiment at the University of Southern Queensland that goes astray, with tragic results. An effort to breed meatier chickens somehow produces an intelligent, 200 kilogram chicken that escapes from the lab and terrorises the campus. In a surprise ending the chicken is befriended by coach Tim Galvano, who teaches it how to play Rugby and help his team win State, National and World Championships. Because of the movie’s controversial nature, it has the potential to be either a smash hit, a modest success, or a total bomb. International is trying to decide whether to release the picture for general distribution initially or to start out with a ‘limited first-run release’ at a few selected theatres, followed by general distribution after 3 months. The company has estimated the following probabilities and conditional profits for ‘Claws’:
PROFITS (Millions of \$)
Level of Limited General success Probability release distri

Smash .3 22 12
Modest .4 9 8
Bomb .3 –10 –2

International can run sneak previews of ‘Claws’ to get a better idea of the movies’ ultimate level of success. Preview audiences rate movies as either good or excellent. On the basis of past experiences, it was found that 90% of all smash successes were rated excellent (and 10% rated good), 75% of all modest successes were rated excellent (25% rated good) and 40% of all bombs were rated excellent (60% rated good). The cost of running sneak previews is not cheap. Currently, this stands at \$1m.
QUESTION 25
What is the opportunity loss for a Limited release for a Modest level of success?
Answer should be to whole numbers only. You do not need to put any units in your answer.

QUESTION 26
What would the optimal action be for International before running the sneak preview?

Run a limited release with an expected payoff of \$7.20m

Run a limited release with an expected payoff of \$6.20m

Run a general distribution with an expected payoff of \$7.20m

Run a general distribution with an expected payoff of \$6.20m

QUESTION 27
What is the maximum amount of money that International would be prepared to pay for an absolutely reliable forecast of the movies’ level of success?

\$9.6m

\$7.2m

\$6.2m

\$2.4m

QUESTION 28
What would be the joint probability for a ‘bomb success’ and excellent preview given that in the past, it was found that 40% of all bomb successes were rated excellent?
Answer should be to two decimal places e.g. 0.12, 0.23, etc.

QUESTION 29
What is the posterior probability of a bomb given the sneak preview indicates excellent?
Answer should be to four decimal places e.g. 0.1234, 0.2345 etc.

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