QUESTION 5 Suppose that twelve percent of borrowers of payday loans default on their payments. A random sample of seven borrowers is selected. (Hint: use the binomial distribution for this question, first defining what a success or trial is). Match each questions with the relevant answer. What is approximately the probability that exactly one borrower in the sample will default on her/his payments? A. 0.39 - > What is approximately the probability that at most one borrower in the sample will default on their payments? [Hint: at most one borrower means B. 0.80 no more than one borrower, that is, one, or fewer, borrowers] C. 0.84 - What is approximately the probability that exactly six borrowers in the sample will not default on their payments? - What is the expected number of defaults in this random sample of seven borrowers? QUESTION 6 Consider a random variable with a binomial distribution, with 18 trials and probability of success equals to 0.29. The expected value of this random variable is equal to: (Use two decimals in your answer) QUESTION 7 Suppose a stock has returns that are normally distributed, with an average annual return of 8% and a standard deviation of 3%. - What percent of years does this stock have a return between 5% and 11%? A. 68% - What percent of years does this stock have a return between 2% and 14%? B. 95% What percent of years does this stock have a return between - 1% and 17%? C. 09.7% QUESTION 8 Suppose that X is a normally distributed random variable, with mean 10 and standard deviation 2. What is the probability that X has a value greater than 10.8? O 0.2504 O 0.6554 O 0.3446 O 0.853 QUESTION 9 X is a normal random variable with mean equal to -10 and standard deviation equal to 8. Suppose we observe a value of X equal to -16.9. What is the Z-score of this observation? (Enter two decimals for your answer) QUESTION 10 The number of ways to choose 6 successes out of 10 trials, in symbols (10) 6 . is equal to: O 210 O 125 O 60 O None of the above