USE A CALCULATOR In the 1992 presidential election, Alaska’s 40 election districts averaged 1,956.8 votes per district for President Clinton. The standard deviation was 572.3. (There are only 40 election districts in Alaska.) The distribution of the votes per district for President Clinton was bell-shaped. Let X = number of votes for President Clinton for an election district. State the approximate distribution of X. Is 1,956.8 a population mean or a sample mean? How do you know? Find the probability that a randomly selected district had fewer than 1,600 votes for President Clinton. Sketch the graph and write the probability statement. Find the probability that a randomly selected district had between 1,800 and 2,000 votes for President Clinton. Find the third quartile for votes for President Clinton.
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!
USE A CALCULATOR
In the 1992 presidential election, Alaska’s 40 election districts averaged 1,956.8 votes per district for President Clinton. The standard deviation was 572.3. (There are only 40 election districts in Alaska.) The distribution of the votes per district for President Clinton was bell-shaped. Let X = number of votes for President Clinton for an election district.
- State the approximate distribution of X.
- Is 1,956.8 a population
mean or a sample mean? How do you know? - Find the
probability that a randomly selected district had fewer than 1,600 votes for President Clinton. Sketch the graph and write the probability statement. - Find the probability that a randomly selected district had between 1,800 and 2,000 votes for President Clinton.
- Find the third
quartile for votes for President Clinton.
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