The report "New Study Shows Need for Americans to Focus on Securing Online Accounts and Backing up Critical Data" (PRNewswire, October 29, 2009) states that only 25% of Americans change computer passwords quarterly, in spite of a recommendation from the National Cyber Security Alliance that passwords be changed at least once every 90 days. For purposes of this exercise, assume that the 25% figure is correct for the population of adult Americans.
a. If a random sample of 20 adult Americans is selected, what is the probability that exactly 3 of them change passwords quarterly?
b. What is the probability that more than 8 people in a random sample of 20 adult Americans change passwords quarterly?
c. What is the mean and standard deviation of the variable x 5 number of people in a random sample of 100 adult Americans who change passwords quarterly?
d. Find the approximate probability that the number of people who change passwords quarterly in a random sample of 100 adult Americans is less than 20.