Uncements This Question: 4 pts
The results of a recent mayoral election are shown in the table
Candidate Frequency
Ford
494
272
Anderson
Garcia
424
285
Wong
If one voter is chose at random, what is the probability the she voted for Anderson? Round your answer to the nearest thousandth when necessary
OA. 0.184
OB. 272
OC. 0.004
OD. 0.229
Click to select your answer.
Previous

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.

the correct answer would be c