A giant vat contains large numbers of two types of bacteria, called strain A and strain B. Assume that 30% of the bacteria in the vat are strain A, and the other 70% are strain B. The vat is well mixed. Twenty technicians each collect a random sample of 15 cells from the vat and then determine which strain each cell belongs to.

a. What will the proportion of strain A cells be in these 20 samples, on average?

b. Each technician counts the number of strain A bacteria cells in his or her sample. To what distribution should the number of strain A bacteria in samples conform?

c. Each technician counts the proportion of strain A cells in his or her sample. What should the standard deviation be among samples in this proportion?

d. Each technician correctly calculates a 95% confidence interval for the proportion of A cells in the vat. On average, what fraction of technicians will construct an interval that includes the value 0.3?