QUESTION TWO A. The following data set shows the probability distribution for a survey conducted to determine the number of bedrooms in the respondent's household. Number of bedrooms Probability 0.25 4 0.55 5 0.15 0.05 Total (i) Calculate the mean of the probability distribution. [3 Marks] (ii) Calculate the variance and standard deviation of this probability distribution. [4 Marks] B. Suppose a test consists of 10-multiple choice questions and each question has four choices.(i) Calculate the probability that a student who guesses randomly will answer exactly two questions correctly. [4 Marks] (ii) Calculate the probability that a student who guesses randomly will answer fewer than three questions correctly. [4 Marks] C. Suppose a certain retail store has customers whose ages are normally distributed such that p=37.5 years and 6=7.6 years. (i) Calculate the probability that a randomly chosen customer is more than 48 years old. [3 Marks] (ii) Calculate the probability that a randomly chosen customer is younger than 44 years old. [3 Marks] (iii) Calculate the probability that a randomly chosen customer is between 46 and 54 years old. [4 Marks]