Question

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In the 1992 presidential election, Alaska's 40 election districts averaged 2088 votes per district for President Clinton. The standard deviation was 557. (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. a. What is the distribution of X? X-NI b. Is 2088 a population mean or a sample mean? Select an answer c. Find the probability that a randomly selected district had fewer than 2116 votes for President Clinton. d. Find the probability that a randomly selected district had between 2270 and 2562 votes for President Clinton. e. Find the third quartile for votes for President Clinton. Round your answer to the nearest whole number

Answer 1

a) x~ N(2089, 557) (6) 2088 in a population mean. P(X2 2116) 0.5199 We well use a table and standard normal distribution 7 PLZL 2116-2088 2 Plzco.rs) 557 a 2270 L XL 2562 DP 42 2562-2088 P(AL2s - PZL 2270-2088 P/7 557 557 PlzL0.85 t2015) - 10.0.38) 0.802 - 0.62932 0.173. the need @z for rodes of President Clinton, Q3 2 75th percentile P(xca) = 0.75 QA corresponding z nalue 557 = uning table. a- 2088 - a - 2088 2 0.67449 92 557x 0.67449+2085 =) a= 24 63-69093 2464 557 2464 votes.