Four-legged animals run with two different types of motion: trotting and galloping. An animal that is trotting has at least one foot on the ground at all times, whereas an animal that is galloping has all four feet off the ground at some point in its stride. The number of strides per minute at which an animal breaks from a trot to a gallop depends on the weight of the animal. Use the table and the method of this example to find an equation that relates an animal's weight x (in pounds) and its lowest galloping speed y (in strides per minute). Weight, x 25 35 50 75 500 1000 Galloping Speed, y 193.5 182.7 174.8 161.2 125.9 114.2 Take the natural logarithm of each coordinate to obtain points of the form (In x, In y). (Round your answers to three decimal places.) Weight, x 25 35 50 75 500 1000 Galloping Speed, y 193.5 182.7 174.8 161.2 125.9 114.2 In x In y Find the least squares regression line for the transformed points. (Round your answers to three decimal places.) In y = In x Find an equation of the form y = axb that relates an animal's weight x (in pounds) and its lowest galloping speed y (in strides per minute). (Round your value for a to one decimal place and your value for b to three decimal places.) y =

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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!