On average, how many spectators will attend? Determine the variance and standard deviation for the number of spectators.
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!
Recall the golf tournament example where the weather for the tournament is classified as “good”, “fair”, or “bad”. Further recall that the weather is “good” 60% of the time, and “fair” 30% of the time. Suppose spectator attendance will be 100,000 if the weather is “good”, 70,000 if the weather is “fair”, and 30,000 if the weather is “bad”. On average, how many spectators will attend? Determine the variance and standard deviation for the number of spectators.
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