A pharmaceutical company is formulating a new medication that prevents painful gout attacks. However, the lead researchers are also mindful of its impacts to the human liver, which can be indicated by monitoring levels of alanine aminotransferase (or ALT, in U/L units) . If the ALT levels exceed an average of 55 U/L, there is an indication of the drug having damaging effects to the liver. Let us assume that ALT levels are normally distributed with standard deviation of 15.7 U/L. To determine the consequence of this new drug, they randomly selected 162 adult men with gout and monitored levels of alanine aminotransferase (or ALT, in U/L units) after taking the new medicine for 6 months. From the sample, it is found that the average ALT level is 59 U/L. It is suspected levels are significantly increased. Conduct a test of significance with a=0.05. (Source: Liver function tests. (2019, June 13). Retrieved from https://www.mayoclinic.org/tests-procedures/liver-function-tests/about/pac- 2039459) What is the value of the Z-test statistic? O 3.24 1.23 O 4.00 -3.24 0.25
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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