As part of a promotion for a new type of cracker, free samples are offered to shoppers at a local supermarket. The probability that a shopper will buy a packet of crackers after tasting a free sample is 0.3. Differenst shoppers can be regarded as independent trials. let P^ be the proportion of the next 60 shoppers that buy a packet of crackers after tasting a free sample. a). what is the mean and the standard deviation of the sample distribution? b. what is the probability that more than half the shoppers buy a packet? C.what is the probability that the sample proportion is between 0.2 and 0.4? D. how large should n be so that the standard deviation of P^ is no more than 0.01?