A) suppose bob wants to receive messages using elgamal public cryptosystem. he chooses 181, g-2 and chooses x -5, which he keeps as a secret. what information will he make public? if alice wants to send the message m-31 and chooses k-3, what will she send to bob? if bob receives the pair (9,31) from eve what is the message sent by eve?

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.