In a diagnostic, a student correctly answers about 50% of the questions posed. However, after a full semester, there was 63 points missed out of a total of 150 points attempted; that is, the student answered 87 points correctly. Obtain a 95% confidence interval for the true proportion of correctly answered questions. Interpret your results in the context of the problem. State the margin of error.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is