The total duration of baseball games in the major league in the 2011 season is uniformly distributed between 445 hours and 525 hours inclusive. Find a and b and describe what they represent. Write the distribution. Find the mean and the standard deviation.
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!
The total duration of baseball games in the major league in the 2011 season is uniformly distributed between 445 hours and 525 hours inclusive.
- Find a and b and describe what they represent.
- Write the distribution.
- Find the mean and the standard deviation.
- What is the probability that the duration of games for a team for the 2011 season is between 470 and 500 hours?
- What is the 80th percentile for the duration of games for a team for the 2011 season?
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