According to the research, 45% of homes sold in a certain month and year were purchased by rst-time buyers. A random sample of 165 people whojust purchased homes is selected. Complete parts a through e below. a. Calculate the standard error of the proportion. up = I: (Round to four decimal places as needed.) b. What is the probability that less than 78 of them are rsttime buyers? P(Less than 78 of them are rsttime buyers) = :| (Round to four decimal places as needed.) c. What is the probability that more than 80 of them are rsttime buyers? P(More than 80 of them are rst-time buyers) = (Round to four decimal places as needed.) d. What is the probability that more than 72 of them are rsttime buyers? P(More than 72 of them are rst-time buyers) = (Round to four decimal places as needed.) e. What is the probability that between 64 and 69 of them are rst-time buyers? P(Between 64 and 69 of them are rst-time buyers) = (Round to four decimal places as needed.)