# statistics

posted by
**iyra** on
.

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 theaters, followed by general distribution after 3 months. The company has estimated the following probabilities and conditional profits for ‘Claws’:

PROFITS (Millions of $)

Level of

success Probability Limited General

release distribution

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.

What is the opportunity loss for a General Distribution for a Smash level of success?

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

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

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

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

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

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?

1) $9.6 m

2) $7.2 m

3) $6.2 m

4) $2.4 m

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?

What is the posterior probability of a bomb given the sneak preview indicates good?

What is the maximum amount that should be paid for the sneak preview [i.e. what would be the expected value of sample information (EVSI)]?

1) $1.04 million

2) $2.58 million

3) $7.20 million

4) $8.24 million