A sample of 100 was taken from a population with π = 0.5. Find the probability that the sample proportion will lie between: (a) 0.4 and 0.6, (b) 0.35 and 0.65, and (c) 0.5 and 0.65. From a...

A sample of 100 was taken from a population with π = 0.5. Find the probability that the sample proportion will lie between: (a) 0.4 and 0.6, (b) 0.35 and 0.65, and (c) 0.5 and 0.65.

From a parliamentary constituency a sample of 100 people were asked whether they would vote Labour or Conservative. It is thought that 40% of the constituency will favour Labour. Find the approximate probability that in an election Labour will win (assume only a two-party vote).