The weight of an organ in adult males has a bell-shaped distribution with a mean of 310 grams and a standard deviation of 20 grams. Use the empirical rule to determine the following (a) About 68% of organs will be between what weights? (b) What percentage of organs weighs between 270 grams and 350 grams? (c) What percentage of organs weighs less than 270 grams or more than 350 grams? (d) What percentage of organs weighs between 270 grams and 370 grams? (a)and grams (Use ascending order.)
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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According to the empirical rule, approximately 68% of the observations fall within 1 standard deviation of the mean. For this case,
=μ±σ
= 310±20
=(290,330)
Hence, it can be said that approximately 68% of the observations fall between 290 and 330 grams.
According to the empirical rule, approximately 95% of the observations fall within 2 standard deviations of the mean. For this case,
= μ±2σ
= 310±2*20
= (270,350)
Hence, it can be said that approximately 95% of the observations fall between 270 and 350 grams.
The percentage of organs weighs less than 270 grams or more than 350 grams is 5%, as approximately 95% of the observations fall between 270 and 350 grams.
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