The mean amount of time it takes a kidney stone to pass is 14 days and the standard deviation is 5 days. Suppose that one individual is randomly chosen. Let X = time to pass the kidney stone. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N( , ) b. Find the probability that a randomly selected person with a kidney stone will take longer than 17 days to pass it. c. Find the minimum number for the upper quarter of the time to pass a kidney stone. ___________ 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!
The mean amount of time it takes a kidney stone to pass is 14 days and the standard deviation is 5 days. Suppose that one individual is randomly chosen. Let X = time to pass the kidney stone. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N( , )
b. Find the probability that a randomly selected person with a kidney stone will take longer than 17 days to pass it.
c. Find the minimum number for the upper quarter of the time to pass a kidney stone. ___________ days.
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