The heights of women have a symmetric distribution with a mean of 63 inches and a standard deviation of 3 inches. 1. Approximately 68% of women have heights between )inches. 2. Approximately 95% of women have heights between inches. 3. Approximately 99.7% of women have heights between ) inches.
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!
It is given that the heights of women follows a normal distribution with a mean 63 inches and a standard deviation 3 inches.
Empirical rule:
- Approximately 68% of the data falls within one standard deviation.
- Approximately 95% of the data falls within two standard deviations.
- Approximately 99.7% of the data falls within three standard deviations.
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