Researchers are interested in estimating the prevalence of maternal smoking habits while pregnant. There are countless advertisements warning such behavior, and recent statistics claim the prevalence of such behavior is quite low, at only 5%. Suppose the research team is planning a study to promote further intervention to decrease what they believe is a rising prevalence of the behavior. Suppose they sample 107 pregnant mothers in their third trimester and determine that 12 mothers have smoked at least once during their pregnancy. Calculate the probability of observing the results that were witnessed in the sample.
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!
Researchers are interested in estimating the prevalence of maternal smoking habits while pregnant. There are countless advertisements warning such behavior, and recent statistics claim the prevalence of such behavior is quite low, at only 5%. Suppose the research team is planning a study to promote further intervention to decrease what they believe is a rising prevalence of the behavior. Suppose they sample 107 pregnant mothers in their third trimester and determine that 12 mothers have smoked at least once during their pregnancy.
Calculate the probability of observing the results that were witnessed in the sample.
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