The manager of a clothing shop wishes to investigate how satisfied customers are with the quality of service they receive. A database of the shop's customers is used as a sampling frame for this investigation.
Identify one potential problem with this sampling frame.
Customers are asked to complete a survey about the quality of service they receive. Past information shows that \(35 \%\) of customers complete the survey.
A random sample of 20 customers is taken.
Write down a suitable distribution to model the number of customers in this sample that complete the survey.
Find the probability that more than half of the customers in the sample complete the survey.