Suppose the lengths of all fish in an area are normally distributed, with mean ? = 31 cm and standard deviation ? = 5 cm. What is the probability that a fish caught in an area will be between the following lengths? (Round your answers to four decimal places.) (a) 31 and 36 cm long (b) 25 and 31 cm long You may need to use the table of areas under the standard normal curve from the appendix.
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!
Suppose the lengths of all fish in an area are
(b) 25 and 31 cm long
You may need to use the table of areas under the standard normal curve from the appendix.
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