Suppose we want to estimate the concentration (ug/mL) of a specific dose of ampicillin in the urine after various periods of time. We recruit 25 volunteers who have received ampicillin and find they have a mean concentration of 7.0 µg/mL with a standard deviation of 2.0 ug/mL. Assume the underlying population distribution of concentrations is normally distributed. a) Find a 95% CI for the population mean concentration. b) Find a 99% CI for the population variance of the concentrations. c) How large a sample would be needed to ensure that the length of the CI in part (a) is 0.5 ug/mL assuming the sample standard deviation remains at 2.0 ug/mL?
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!
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