The Governor Services of England is in the first stage of approving a list of job applications for the position of general clerk for two different departments. If they take a random sample of a mixture of these applications from the two departments, the distribution of the number of applications will be bimodal.

a) As their sample size increases, what is the expected shape of the distribution of the number of applications in the sample?

b) As the sample size increases, what is the expected shape of the sampling model for the mean number of applications of the sample?