A mail-order firm has a circular which elicits a 10% response rate. Suppose 20 of the circulars are mailed as a market test in a new geographic area. Assuming that the 10% response rate is applicable in the new area, determine the probability that
(i) no one responds,
(ii) exactly two people respond,
(iii) less than 20% of the people respond.
The packaging process in a breakfast cereal company has been adjusted so that an average of 13.0 oz of cereal is placed in each package. Of course, not all packages have precisely 13.0 oz because of random sources of variability. The standard deviation of the actual net weight is 0.1 oz and the distribution of weights is known to follow the normal probability distribution.
(i) What is the probability that the weight of the cereal will exceed 13.25 oz?
(ii) Evaluate the probability that a randomly chosen package will contain between 13.0 and 13.2 oz of cereal.