8.22 Operations growth in Luxembourg According to a survey conducted by KPMG in 2016, almost 46% of the surveyed companies intend to grow their operations in Luxembourg over the next two years (Source:

https://www.kpmg.com/LU/en/IssuesAndInsights/

Articlespublications/Documents/Management-

Company-CEO-Survey-032016.pdf).

a. Can you specify the assumptions made to construct a 95% confidence interval for the population proportion?

b. If the sample size is 5000, verify that the assumptions of part a are satisfied and construct the 95% confidence interval. Determine whether the proportion of companies who intend to grow their operations in Luxembourg is a majority or a minority.