A research paper describes a study of the relationship between age and 1-hour swimming performance. Data on age and swim distance for over 10,000 men participating in a national long-distance 1-hour swimming competition are summarized in the accompanying table. ITT Representative Age (Midpoint of Age Group) Average Swim Distance (meters) Age Group 20-29 25 3913.5 30-39 35 3718.8 40-49 45 3579.4 50-59 55 3351.9 60-69 65 3000.1 70-79 75 2639.0 80-89 85 2118.4 (a) Find the equation of the least-squares line with x = representative age and y = average swim distance. (Round your numerical values to three decimal places.) ŷ = 4791.696 x +( -29.015 (b) Compute the seven residuals. (Round your answers to three decimal places.) Representative Age (x) Residual (meters) 25 -152.821 35 -37.371 45 93.379 55 166.029 65 94.379 75 43.429 85 -207.021

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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!