Question: Sikhism, a religion founded in the 15th century in India, is going through turmoil due to a rapid decline in the number of Sikh youths who wear turbans (Washington Post, March 29, 2009). The tedious task of combing and tying up long hair and a desire to assimilate has led to approximately 25% of Sikh youths giving up the turban.
a. What is the probability that exactly two in a random sample of five Sikh youths wear a turban?
b. What is the probability that two or more in a random sample of five Sikh youths wear a turban?
c. What is the probability that more than the expected number of Sikh youths wear a turban in a random sample of five Sikh youths?
d. What is the probability that more than the expected number of Sikh youths wear a turban in a random sample of 10 Sikh youths?