You are the owner of Normal's Cattle Ranch. The weights of steers in the herd are normally distributed with a mean of 900 pounds and a standard deviation of 120 pounds. What is the probability that the average weight for a sample of 40 steers from this herd will be within 25 pounds of the mean weight of all steers from his herd? (round to three decimal places).
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!
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