Nine percent of men and 0.25% of women cannot distinguish between the colors red and green. This is the type of color blindness that causes problems with traffic signals.
a. If six men are randomly selected for a study of traffic signal perceptions, find the probability that exactly two of them cannot distinguish between red and green. Use the binomial probability formula and verify that the assumptions are satisfied.
b. Researchers need at least 50 men with this type of colorblindness, so they randomly select 600 men for a study of traffic-signal perceptions. Estimate the probability that at least 50 of the men cannot distinguish between red and green. Is the result high enough so that the researchers can be very confident of getting at least 50 men with red and green colorblindness?