The mean incubation time for a type of fertilized egg kept at a certain temperature is 16 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 2 days. Complete parts​ (a) through​ (e) below. ​(a) Find and interpret the probability that a randomly selected fertilized egg hatches in less than 14 days.   The probability that a randomly selected fertilized egg hatches in less than 14 days is nothing. ​(Round to four decimal places as​ needed.)   ​(b) Find and interpret the probability that a randomly selected fertilized egg takes over 18 days to hatch.   The probability that a randomly selected fertilized egg takes over 18 days to hatch is nothing. ​(Round to four decimal places as​ needed.)   ​(c) Find and interpret the probability that a randomly selected fertilized egg hatches between 12 and 16 days.   The probability that a randomly selected fertilized egg hatches between 12 and 16 days is nothing. ​(Round to four decimal places as ​needed.) ​(d) Would it be unusual for an egg to hatch in less than 10 ​days? Why?   The probability of an egg hatching in less than 10 days is nothing​, so it ▼   would not would be​ unusual, since the probability is ▼   greater less than 0.05. ​(Round to four decimal places as​ needed.)

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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!