New Skiers Come to Learn to Ski on the Semi-Dangerous

question 6

Essay

New skiers come to learn to ski on the semi-dangerous slopes of Northeastern Iowa.
On Big Bunny Slope skiers will sometimes fail to make the turn at Big Bend. On
Little Bunny Slope, skiers will sometimes tumble at Little Hill. The ski instructors
send a randomly selected group of 25 new skiers down each slope, wait a few
moments, and then send the Ski Patrol Ambulance down after them, stopping at Big
Bend to gather those who don't make the turn and then Little Hill to gather those who
tumble. The skiers descend the slopes far enough apart that they don't run into each
other, so their runs down the slopes are all independent.
a) The probability that a new skier will not make the turn at Big Bend is 0.3. If we
define the random variable B = number of new skiers in a group of 25 needing to
be driven to the First Aid Station from Big Bend, we can model this situation as a
binomial chance experiment. What are the mean and standard deviation of B?
b) The probability that a new skier will tumble at Little Hill is 0.1. If we define the
random variable L = number of new skiers in a group of 25 needing to be driven
to the First Aid Station from Little Hill, we can model this situation as a binomial
chance experiment. What are the mean and standard deviation of L?
c) Consider an instance of the instructors sending one group down Big Bunny Slope,
and one group down Little Bunny Slope. The total number of injuries requiring
the ambulance, T, is the random variable formed by calculating B + L. Using
your results from (a) and (b), calculate 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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