a) Research has shown at 55% of subscribers share their password with someone outside of their household. A random sample of 12 persons were sampled. i. Define the variable of interest for this scenario. [1] ii. What probability distribution do you think best describes the situation? Why? [5] . . . 111. Calculate the probability that less than 3 subscribers will share their password. [2] iv . If 500 persons were sampled, determine the number of persons who are expected to share their password with someone outside of their household. [2] b) The number of bacterial colonies on a petri dish can has an average of 2.5 per cm2. i. Define the variable of interest for this scenario. [1] ii. What probability distribution do you think best describes the situation? Why? [4] iii. Calculate the mean and standard deviation of the distribution [2] iv. Find the probability that a) in 1 cm there are no bacterial colonies b) in 4 cm there are more than three bacterial colonies