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?

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Definitions:

Depression

A common and serious medical illness that negatively affects how one feels, thinks, and acts, leading to feelings of sadness and/or a loss of interest in activities once enjoyed.

Anorexia Nervosa

An eating disorder characterized by an obsessive fear of gaining weight, leading to severe restrictions on food intake and extreme weight loss.

Fatal

Resulting in death or having a very severe outcome with irreversible consequences.

High-Fat Foods

Refer to foods that are rich in fats, often associated with increased calories and potential health impacts when consumed excessively.