A computer scanner can read a bar code on a package correctly 97% of the time. One company monitors the accuracy of the scanner by randomly sampling packages and verifying that each package has been correctly scanned. Random samples of size n = 25, 50, 100, and 200 have recently been taken with the following results:

Sample Size, n ................................... Number Correctly Scanned
25 ............................................................................... 24
50 ............................................................................... 49
100 ............................................................................. 95
200 ........................................................................... 193

a. For each sample size, calculate the sample proportion.
b. For each sample size, what are the mean and standard deviation of the sampling distribution?

c. Calculate the single-proportion sampling error for each sample size. 

d. For a sample of size n = 200, what is the probability of finding 198 correctly scanned packages?