Question 3 (6 marks) Marks A random sample of 150 approved mortgage applications is selected from a bank's database. Customers of this bank can choose either variable or interest-only mortgages. These mortgage choices have either a 20-year or 30-year term. The data are displayed in the table below. Type of Mortgage Variable Interest Only Total Use the table above to answer the questions below. i. If an approved application is selected at random, what is the probability that it is a 30-year term application? [1] ii. If an approved application is randomly selected, what is the probability that the mortgage choice is variable and has a term of 20 years or is interest only and has a term of 20 years? [2] Question 3 (continued) Marks b. The table below shows the probability distribution of the number of stores visited per customer per single visit to the mall. Assume that a customer can visit at most four stores per single visit to the mall. Number of stores visited Probability per customer per single P(x) xPCI) (x u)2P(x) visit (at) 0 0.04 1 0.41 2 0.40 3 0.09 4 0.06 i. Using the table above, compute the expected number of stores visited per customer per single visit to the mail for the above distribution. [1] ii. Using the table above, compute the standard deviation for the above distribution. [2]