An official from the downtown development authority claims that the percentage of local businesses that have had some growth in the past year is 50%. A random sample of 44 local businesses is taken, and they were asked whether they have grown over the past year.
a.) What is the probability that 60% or more of the sampled businesses have experienced some growth over the past year?
b.) Is this a rare event? (happens less than 5% of the time)