A polling agency reported that the proportion of 12th grade students who are engaged is 0.34. Engagement is defined as​ students' involvement and enthusiasm with school. The superintendent of one high school district believes the engagement of her students is higher than the proportion reported. She randomly surveys 90 of the 3600 students in the district and finds that 38 reported being engaged in school. Complete parts​ (a) through​ (e) below. ​(a) What type of variable is​ "engaged"? The variable is qualitative. ​(b) What is the sample proportion of students in this high school district who are​ engaged? p=0.42220.4222 ​(Round to four decimal places as​ needed.) ​(c) Verify that the distribution of the sample proportion is approximately normal. The sample​ size, n=9090​, is less than ​5% of the population​ size, or 0.05N=180180. ​(Type integers or decimals. Do not​ round.) For this​ sample, np1−p=nothing less than or equals≤ 10.