A housing survey was conducted to determine the price of a typical home in Topanga, CA. The mean price of a house was roughly $1.3 million with a standard deviation of $300,000. There were no houses listed below $600,000 but a few houses above $3 million. (a) Is the distribution of housing prices in Topanga symmetric, right skewed, or left skewed? Hint: Sketch the distribution. symmetric left skewed right skewed (b) Would you expect most houses in Topanga to cost more or less than $1.3 million? less more (c) What is the probability that the mean of 60 randomly chosen houses in Topanga is more than $1.4 million?
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 housing survey was conducted to determine the price of a typical home in Topanga, CA. The mean price of a house was roughly $1.3 million with a standard deviation of $300,000. There were no houses listed below $600,000 but a few houses above $3 million.
(a) Is the distribution of housing prices in Topanga symmetric, right skewed, or left skewed? Hint: Sketch the distribution.
- symmetric
- left skewed
- right skewed
(b) Would you expect most houses in Topanga to cost more or less than $1.3 million?
- less
- more
(c) What is the
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