Suppose the heights of Australian adult males are normally distributed with a population mean of 174 cm and a population variance of 25 cm2. Let X denote the height of a randomly selected Australian adult male. Let X¯denote the mean height of 100 males randomly selected from the Australianadult male population i)State the distribution of X¯in conventional statistical notation. ii)What is the probability that X¯is greater than or equal to 172.5 cm?
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!
- Suppose the heights of Australian adult males are
normally distributed with a population mean of 174 cm and a population variance of 25 cm2. Let X denote the height of a randomly selected Australian adult male. Let X¯denote the mean height of 100 males randomly selected from the Australianadult male population
i)State the distribution of X¯in conventional statistical notation.
ii)What is the probability that X¯is greater than or equal to 172.5 cm?
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