A random sample of 1000 people was taken. Four hundred fifty of the people in the sample favored Candidate AT. The 95% confidence interval for the true proportion of people who favor Candidate A is a. .424 to .476. b. .419 to .481. c. .40 to .50. d. .45 to .55.

And the 95% confidence interval would be given (0.419;0.481).   And the best option would be:

b. .419 to .481

Step-by-step explanation:

We know the following info:

sample size selected

represent the number of people who favored Candidate AT

The sample proportion would be:

The confidence interval would be given by this formula  

For the 95% confidence interval the value of and , with that value we can find the quantile required for the interval in the normal standard distribution.  

And replacing into the confidence interval formula we got:  

And the 95% confidence interval would be given (0.419;0.481).   And the best option would be:

b. .419 to .481

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm