Question

In the 1992 presidential election, Alaska's 40 election districts averaged 2199 votes per district for
President Clinton. The standard deviation was 588. (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.

c. Find the probability that a randomly selected district had fewer than 2052 votes for President Clinton.

d. Find the probability that a randomly selected district had between 2370 and 2600 votes for President Clinton.

e. Find the first quartile for votes for President Clinton. Round your answer to the nearest whole number.

Answer 1

Answer:

Step-by-step explanation:

this is a normal distribution with mean= 2199 and standard deivation= 588

c. we want P(x<2052) standardize (2052-2199)/588= -.25

Go to a ztable and find .25= 0.5987 and then take the compliment

1-0.5987=.4013

d. P(2370<x<2600)= P(x<2600)-P(x<2370)

(2600-2199)/588= .68 = 0.7517

(2370-2199)/588= .29 = .6141

.7517-.6141= .1376 (if this is wrong try .138)

e. first quartile= 25th percentile

25th percentile has a zscore of -.675

-.675=(x-2199)/588

x=1802.1 = 1802