A researcher wants to make a 99% confidence interval for a population proportion. A preliminary sample produced the sample proportion of 0.46. The sample size that would limit the margin of error to be within 0.061 of the population proportion is:

the sample size that would limit margin of error is 443

Step-by-step explanation:

The confidence level = 99 percent = 0.99

1 - alpha = 0.99

Alpha = 1 - 0.99

= 0.01

The critical z value for alpha = 0.01 = 2.576

Sample proportion = 0.46

Margin of error E = 0.061

Sample size = p(1-p)(Z/E)²

= 0.46(1-0.46) x (2.576/0.061)²

= 0.46(0.54)(42.23)²

= 0.2484 x 1783.37

= 442.989

= 443

The sample size would be 443

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

answer:

125 yards

explanation:

75+50=125. that is my answer