Suppose that skiing injuries occur at a constant rate, are statistically independent of each other, and the amount of time required to treat each injury follows an approximately normal distribution with a mean of 80 minutes and a standard deviation of 20 minutes. Assume the average ski injury rate is 2.6 injuries per 1,000 skier-days, and the treatment time is independent of the number of injuries treated on any day. a. In a week with 150 skiers each day, what is the probability there is at least 1 injury on each day? b. In a week with 150 skiers each day, what is the probability there is at least 1 injury on at least 5 of the 7 days? c. On a day with 7 injuries, what is the probability that at least 5 of the 7 injuries require more than 100 minutes to treat the injury? d. In a week with 7 injuries, what is the probability that at least 5 of the 7 injuries require more than 100 minutes to treat the injury?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Suppose that skiing injuries occur at a constant rate, are statistically independent of each other, and the amount of time required to treat each injury follows an approximately
a. In a week with 150 skiers each day, what is the
b. In a week with 150 skiers each day, what is the probability there is at least 1 injury on at least 5 of the 7 days?
c. On a day with 7 injuries, what is the probability that at least 5 of the 7 injuries require more than 100 minutes to treat the injury?
d. In a week with 7 injuries, what is the probability that at least 5 of the 7 injuries require more than 100 minutes to treat the injury?
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