Chapter 6. In the 2020 presidential election, Texas' 36 election districts averaged 146,087 votes per district for Joe Biden. The standard deviation was 47,073. (There were only 36 election districts in Texas in 2020.) Let us assume that the distribution of the votes per district for Biden was bell-shaped. Let X = number of votes for Biden in an election district. Unless specified, round all numbers to nearest whole number.

1. The approximate distribution of X is X ~N( , )
2. Is 146,087 votes a population mean or a sample mean?
3. Find the probability (in % terms) that a randomly selected district had fewer than 100,000 votes for Biden. %
4. Find the probability (in % terms) that a randomly selected district had between 140,000 and 180,000 votes for Biden. %
5. Find the first quartile of votes for Biden.