Pregnancy Assume that the duration of human pregnan-cies can be described by a Normal model with mean 266 days and standard deviation 16 days.a) What percentage of pregnancies should last between270 and 280 days?b) At least how many days should the longest 25% of allpregnancies last?c) Suppose a certain obstetrician is currently providingprenatal care to 60 pregnant women. Let y representthe mean length of their pregnancies. According to theCentral Limit Theorem, what’s the distribution of this sample mean, y? Specify the model, mean, and stan-dard deviation. d) What’s the probability that the mean duration of thesepatients’ pregnancies will be less than 260 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!
cies can be described by a Normal model with mean 266
a) What percentage of pregnancies should last between
270 and 280 days?
b) At least how many days should the longest 25% of all
pregnancies last?
c) Suppose a certain obstetrician is currently providing
prenatal care to 60 pregnant women. Let y represent
the mean length of their pregnancies. According to the
Central Limit Theorem, what’s the distribution of this
dard deviation.
patients’ pregnancies will be less than 260 days?
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