The lengths of a particular animal's pregnancies are approximately normally distributed, with mean p = 266 days and standard deviation o = 16 days. (a) What proportion of pregnancies lasts more than 286 days? (b) What proportion of pregnancies lasts between 258 and 274 days? (c) What is the probability that a randomly selected pregnancy lasts no more than 262 days? (d) A "very preterm" baby is one whose gestation period is less than 242 days. Are very preterm babies unusual? (a) The proportion of pregnancies that last more than 286 days is (Round to four decimal places as needed.)
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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