A store has determined that 30% of all lawn mower purchasers will also purchase a service agreement. In 1 month 280 lawn mowers are sold to customers, who can be regarded as a random sample of all purchasers.
a. What is the standard error of the sample proportion of those who will purchase a service agreement?
b. What is the probability that the sample proportion will be less than 0.32?
c. Without doing the calculations, state in which of the following ranges the sample proportion is most likely to be: 0.29 to 0.31, 0.30 to 0.32, 0.31 to 0.33, or 0.32 to 0.34.