In the Somewhat Less Than Towering Ski Slopes of Northeastern

question 33

Essay

In the somewhat less than towering ski slopes of northeastern Iowa new skiers come to learn to ski. On Big Bunny Slope skiers will fail to make the turn at Big Bend. On Little Bunny Slope, skiers will sometimes tumble at Little Hill. The ski instructors send the new skiers down the two slopes in groups of 25, wait a few moments, and then send the Ski Patrol Ambulance down after them, stopping at Big Bend and then Little Hill. The skiers descend the slopes far enough apart that they don't run into each other, so their spills are all independent.
a) The probability that a random new skier in the group will need to be carried to the First Aid Station after a spill at Big Bend is 0.3. If we define the random variable B = number of new skiers needing to be driven to the First Aid Station from Big Bend, we can model this situation as a binomial chance experiment. What is the mean and standard deviation of B?
b) The probability that a random new skier in the group will need to be carried to the First Aid Station after a spill at Little Hill is 0.1. If we define the random variable L = number of new skiers needing to be driven to the First Aid Station from Little Hill, what is the mean and standard deviation of L?
c) The total number of injuries requiring the Ambulance, T, is a random variable formed by calculating B + L. What are the mean and standard deviation of the random variable T?
d) When the 25 skiers are sent down from the top of Big Bunny Slope, they are sent one at a time. What is the probability that the first one needing the Ambulance is the 7th one to be sent down the slope?

---

Definitions:

Social Optimum

The most efficient allocation of resources, resulting in the maximization of social welfare and benefiting all members of a society.

Corrective Tax

Levies imposed to address and ameliorate the negative externalities generated by certain economic activities, thereby realigning social and private costs.

Subsidy

A financial contribution granted by the government or a public body to support businesses, reduce the price of commodities, or encourage activities beneficial to the public interest.

Equilibrium Number

When market demand equals supply, leading to stability in prices.