Big Town Fisheries recently stocked a new lake in a city park with fish of various sizes. The distribution of the lengths of these fish is approximately normal with a mean of 8 inches and a standard deviation of 2 inches. Blank #1: Find the probability that an individual fish has a length that is greater than 10 inches. Report your answer with four decimal places. It is recommended that you draw, label and shade the distribution of the individuals to aid with your work. Blank #2: Find the probability that the mean of a random sample of 25 fish has a length that is greater than 10 inches. By Central Limit Theorem, the sample means are normal with mean 8 inches and standard deviation 2/5 or 0.4. Report your answer with four decimal places. It is recommended that you draw, label and shade the distribution of the means to aid with your work. Blank #3: Suppose the distribution of fish lengths in this lake was non-normal but had the same mean and standard deviation. Of the two probabilities you computed in blanks 1 & 2, which ones would you still be able to compute? Enter your answer as 1 or 2 or both or none. Blank # 1 Blank # 2 Blank # 3
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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