A medical researcher selects a random sample of 10 small hospitals in a particular state to see if there is a relationship between the number of hospital beds and the number of personnel employed by the hospital. The data are summarized. # of Beds 28 (x) # of Personnel 56 34 42 45 78 84 36 74 95 72 195 74 211 145 139 184 131 233 366 (у) Blank #1: Sketch a scatterplot and describe the relationship you see. Is it linear or non-linear? Is it positive or negative? Is it weak or strong? Give your answer as a list of 3 items to answer these 3 questions, separated by a comma and no extra spaces. For example, a valid answer might look like linear,negative,weak. Blank #2: Write the equation of the regression line, rounding coefficients to two decimal places. Make sure your answer is in equation form, using the variables x and y as appropriate with no extra spaces or parentheses. Blank #3: Should you use the model to make a prediction for the number of personnel for a hospital with 70 beds? (yes or no). Regardless of your answer to that question, use your model to make that prediction and round your answer to the nearest whole number. Enter your answer as a list of two things here: either yes or no,prediction with no extra spaces. For example, a valid answer might look like no,100. Blank #4: Regardless of your description of this relationship, you should not use the model to predict the number of personnel for a hospital with 500 beds because that is and should be avoided.
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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