The weight of an organ in adult males has a bell-shaped distribution with a mean of 310 grams and a standard deviation of 40 grams. Use the empirical rule to determine the folowing (a) About 99.7% of organs will be between what weights? (b) What percentage of organs weighs between 230 grams and 390 grams? (c) What percentage of organs weighs less than 230 grams or more than 390 grams? (d) What percentage of organs weighs between 270 grams and 430 grams? (a)and grams (Use ascending order.) (b)% (Type an integer or a decimal.) (c) % (Type an integer or a decimal.) (d) % (Type an integer or decimal rounded to two decimal places as needed.)
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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Given information:
a)
According the empirical rule 99.7% of the data lies between 3 standard deviation below and above the mean.
z1 = - 3.0
z2 = 3.0
By applying normal distribution:-
x1 = 190
x2 = 430
About 99.7% of organs will weighs between 190 grams and 430 grams.
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