Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Use the 68.95–99.7 rule to find the percentage of buyers who paid: A) Between $149,1000 and $150,900 if the standard deviation is $900 B) between $150,000 and $153,800 if the standard deviation is $1900
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!
a.
Empirical rule:
- The probability that the observation under the normal curve lies within 1 standard deviation of the mean is approximately 0.68.
- The probability that the observation under the normal curve lies within 2 standard deviations of the mean is approximately 0.95.
- The probability that the observation under the normal curve lies within 3 standard deviations of the mean is approximately 0.997.
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