In a town, the brand name of a certain jazz band has a 50% recognition rate. (In other words, a resident of this town selected at random knows about the jazz band with a probability of 0.5.) An executive manager of the band wants to double-check the recognition rate as the band is interested in giving concerts in the town. He/she selects a random sample of 10 residents.

a) Find the (perhaps, approximate) value of the probability that exactly 5 out of ten residents recognize the jazz band.