A Grade I wrist sprain is considered to be a mild injury, where the recovery time is normally distributed with an average of 22 days and a standard deviation of 6.5 days. a) A random person is diagnosed with a Grade I wrist sprain. What is the probability that their recovery time will be between 18 days and 30 days? b) Find the value d so that 85% of all Grade I wrist sprain recovery times fall within the interval (22 − d, 22 + d). c) Suppose 15 random people are diagnosed with a Grade I wrist sprain. What is the probability that at least 2 of them will have a recovery time longer than 29 days? d) Suppose a random sample of 60 people with Grade I wrist sprains have their recovery time measured. What is the probability that the sample average recovery time is less than 21 days?
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!
A Grade I wrist sprain is considered to be a mild injury, where the recovery time is
a) A random person is diagnosed with a Grade I wrist sprain. What is the probability that their recovery time will be between 18 days and 30 days?
b) Find the value d so that 85% of all Grade I wrist sprain recovery times fall within the interval (22 − d, 22 + d).
c) Suppose 15 random people are diagnosed with a Grade I wrist sprain. What is the probability that at least 2 of them will have a recovery time longer than 29 days?
d) Suppose a random sample of 60 people with Grade I wrist sprains have their recovery time measured. What is the probability that the sample average recovery time is less than 21 days?
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