A sport teacher is selecting students who will be attending the school’s Annual Sports Day. He needs to identify students who will qualify for the high jump competition. Based on his past experience, he identifies that the physical constitution, along with light weight, is one of the important factors in winning the competition. A random sample of 35 students’ weight was recorded with 30% of them being in the range of light weight.

a. Based on the data, find a 90% confidence interval for the true proportion of students who are of light weight and who qualify for the high jump competition.

b. If the teacher wants to estimate the population proportion of students in light weight category within a margin of error of {0.1, having the same level of confidence as in part

a, determine the additional number of students he requires for the sample.