The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 260.2 and a standard deviation of 60.5. (All units are 1000 cells/µL.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 78.7 and 441.7? b. What is the approximate percentage of women with platelet counts between 199.7 and 320.7? a. Approximately % of women in this group have platelet counts within 3 standard deviations of the mean, or between 78.7 and 441.7. (Type an integer or a decimal. Do not round.) b. Approximately % of women in this group have platelet counts between 199.7 and 320.7. (Type an integer or a decimal. Do not round.)
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!
Given, the blood platelet counts of group of women have a bell-shaped distribution with a mean of 260.2 and a standard deviation of 60.5.
Now, the 68-95-99.7 emperical rule of standard score states that-
- About 68% of the data values are contained within plus and minus one standard deviation from the mean.
- About 95% of the data values are contained wthin plus and minus two standard deviation from the mean.
- About 99.7% of the data values are contained wthin plus and minus three standard deviation from the mean.
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