Using the Normal Distribution · Exercise 28

In a certain presidential election, Alaska’s 40 election districts averaged 1,956.8 votes per district for Candidate A. The standard deviation was 572.3. (There are only 40 election districts in Alaska.) The distribution of the votes per district for Candidate A was bell-shaped. Let X = number of votes for Candidate A for an election district.

(a) State the approximate distribution of X.
(b) Is 1,956.8 a population mean or a sample mean? How do you know?
(c) Find the probability that a randomly selected district had fewer than 1,600 votes for Candidate A. Sketch the graph and write the probability statement.
(d) Find the probability that a randomly selected district had between 1,800 and 2,000 votes for Candidate A.
(e) Find the third quartile for votes for Candidate A.

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Introductory Statistics 2e · §6.2 Using the Normal Distribution · Exercise 28