In the 1992 presidential election, Alaska's 40 election districts averaged 2123 votes per district for President Clinton. The standard deviation was 554. (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. (Source: The World Almanac and Book of Facts) Round all answers except part e. to 4 decimal places. a. What is the distribution of X? X ~ N(,) b. Is 2123 a population mean or a sample mean? Select an answer Population Mean Sample Mean c. Find the probability that a randomly selected district had fewer than 1994 votes for President Clinton. d. Find the probability that a randomly selected district had between 2060 and 2165 votes for President Clinton. e. Find the third quartile for votes for President Clinton. Round your answer to the nearest whole number.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
In the 1992 presidential election, Alaska's 40 election districts averaged 2123 votes per district for President Clinton. The standard deviation was 554. (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. (Source: The World Almanac and Book of Facts) Round all answers except part e. to 4 decimal places.
a. What is the distribution of X? X ~ N(,)
b. Is 2123 a population mean or a sample mean? Select an answer Population Mean Sample Mean
c. Find the probability that a randomly selected district had fewer than 1994 votes for President Clinton.
d. Find the probability that a randomly selected district had between 2060 and 2165 votes for President Clinton.
e. Find the third quartile for votes for President Clinton. Round your answer to the nearest whole number.
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