Suppose that administrators at a large urban high school want to gain a better understanding of the prevalence of bullying within their school. they select a random sample of 240 students who are asked to complete a survey anonymously. of these students, 54 report that they have experienced bullying. use this information to find a 95% ‑confidence interval for , the true proportion of students at this school who have experienced bullying.

Step-by-step explanation:

Given : Total number of students who are asked to complete a survey anonymously : n= 240

Number of students

The proportion report that they have experienced bullying =54

Then , the proportion that students have experienced bullying =

Significance interval :

Critical value :

The confidence interval for the true proportion is given by :-

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