There are 2,000 eligible voters in a precinct. 500 of the voters are randomly selected and asked whether they planned to vote for the democratic incumbent or the republican challenger. of the 500 surveyed, 350 said they would vote for the democratic incumbent. using the 0.99 confidence coefficient, what are the confidence limits for the proportion that plan to vote for the democratic incumbent?

99% confidence limits for population proportion is:

CL = P +- Z * √(P*(1-P)/N))

Where:

P = sample proportion

Z = Z-score taken at 99% confidence = 2.575

N = sample size

Calculating for the values:
P = 350/500 = 0.7 
N = 500 

Substituting know values to the CL equation:

CL = 0.7 +-  2.575* √(0.7*(1-0.7)/500))

CL = 0.647 , 0.753

Therefore confidence limits range from 0.647 to 0.753.

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;

x = 2

step-by-step explanation:

if sr parallel to ba then the sides bc and ac are in proportion, that is

= ← substitute values

= ( cross- multiply )

27x = 6(4x + 1)

27x = 24x + 6 ( subtract 24x from both sides )

3x = 6 ( divide both sides by 3 )

x = 2