Using the Normal Distribution · Exercise 28

In the 1992 presidential election, Alaska’s 40 election districts averaged 1,956.8 votes per district for a candidate. The standard deviation was 572.3. There are only 40 election districts in Alaska. The distribution of the votes per district for the candidate was bell-shaped. Let X = number of votes for the candidate 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 the candidate. 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 the candidate.
(e) Find the third quartile for votes for the candidate.

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

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