Volunteers who had developed a cold within the previous 24 hours were randomized to take either zinc or placebo lozenges every 2 to 3 hours until their cold symptoms were gone. Twenty-five participants took zinc lozenges, and 23 participants took placebo lozenges. The mean overall duration of symptoms for the zinc lozenge group was 3.5 days, and the standard deviation of overall duration of symptoms was 1.4 days. For the placebo group, the mean overall duration of symptoms was 7.2 days, and the standard deviation was 2 days. (a) Calculate a 95% confidence interval for the mean overall duration of symptoms if everyone in the population were to take the zinc lozenges. (Round your answers to two decimal places.) to days (b) Calculate a 95% confidence interval for the mean overall duration of symptoms if everyone in the population were to take the placebo lozenges. (Round your answers to two decimal places.) to 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!
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