Question

In a certain presidential election, Alaska's 40 election districts averaged 1,958.8 votes per district for a candidate. The standard deviation was 572.5. (There are only 40 election districts in Alaska.) The distribution of the votes per district for one candidate was bell-shaped. Let X = number of votes for this candidate for an election district Parta State the approximate distribution of X. (Enter your numerical values to one decimal place) X-NO Parth Is 1,9588 a population mean or a sample mean? How do you know? A population mean, because all election districts are included A population mean, because only a sample of election districts are included A sample mean, because only a sample of election districts are included. A sample mean, because all election districts are included Part Find the probability that a randomly selected district had fewer than 1,700 votes for this candidate (Round your answer to four decimal places) Sketch the graph 0 1000 2000 3000 4000 1000 2000 3000 4000

Answer 1

1) X will follow the normal distribution , let's find out the parameter for X

X= the number of votes for this candidate per election district

average number of votes for 40districts given to us , mean(x)= 1958.8

standard deviation for 40 districts = 572.5

as there are only 40districts in alaska both these parameteres are population parameteres for our distribution of X

X ~ N(1958.8,572.5)

X ~ N(1958.8 , 572.5)

b) population mean , all districts were included

c)

selected district had fewer than 1700 votes

P(X<1700) = P(X-1958.8/572.5< 1700-1958.8/572,5)

P(Z<-0.45205) = 0.32562

marked sketch graph is correct

d)P(1800<X<2000) = P(1800-1958.8/572.5 < X-1958.8/572.5 < 2000-1958.8/572.5)

P(-0.277 <z<0.072) =0.13781

e) third quartile for vote ~= mean +0.675*standard deviation

third quartile ~ 1958.8 + 0.675*572.5= 2345.23~2345 ~ 4403