Assume that the duration of human pregnancies can be described by a Normal model with mean 266 days and standard deviation 13 days. a) What percentage of pregnancies should last between 271 and 284 days? b) At least how many days should the longest 20% of all pregnancies last? c) Suppose a certain obstetrician is currently providing prenatal care to 48 pregnant women. Let y represent the mean length of their pregnancies. According to the Central Limit Theorem, what's the distribution of this sample mean, y? Specify the model, mean, and standard deviation. d) What's the probability that the mean duration of these patients' pregnancies will be less than 263 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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