Question: When a certain pasta company bags and produces its bags of spaghetti, 5.7% of the pieces of spaghetti end up getting broken. Suppose that 200 pieces of spaghetti that have been bagged are randomly selected and that the number of broken pieces is counted.

a) What is the distribution of the sample proportions that are possible?

b) If the sample proportion is used as a point estimate for the population proportion, what is the expected error of the estimate?

c) What is the chance that the sampling error will be less than 1%?

d) What change would you recommend in the sampling process to increase the chance that the sampling error will be less than 1%?

e) If we increased the sample size to 1000 pieces, then what is the chance that the sampling error will be less than 1%?