In: Statistics and Probability
In the 1992 presidential election, Alaska's 40 election districts averaged 2026 votes per district for President Clinton. The standard deviation was 593. (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 2026 a population mean or a sample mean?
c. Find the probability that a randomly selected district had fewer than 2046 votes for President Clinton. Show all work (including how to get z and how to convert from z table)
d. Find the probability that a randomly selected district had between 2202 and 2334 votes for President Clinton.
e. Find the third quartile for votes for President Clinton. Round your answer to the nearest whole number.