During the 2016 season, the average length of a Houston Astros baseball game was 3 hours, 4 minutes, with a standard deviation of 29 minutes. Assume that the distribution of these game lengths is normal. If a game from that season is selected at random, find the probability that the length of the game is between 2 hours, 30 minutes and 2 hours, 50 minutes. Round your answer to two decimal places. (Hint: Convert game time to minutes format)
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!
During the 2016 season, the average length of a Houston Astros baseball game was 3 hours, 4 minutes, with a standard deviation of 29 minutes. Assume that the distribution of these game lengths is normal. If a game from that season is selected at random, find the
between 2 hours, 30 minutes and 2 hours, 50 minutes. Round your answer to two decimal places. (Hint: Convert game time to minutes format)
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