Over the past 10 years (510 trading weeks), Jane has achieved an average weekly return of 2%, with a weekly standard deviation of 15%.

a. Please calculate the 95% confidence interval of the average return.

b. Please Explain briefly the rationale for your choice of z or t value the above answer.

Jane would like to look at the tail risks and found that around 5% of your 510 weekly returns are below -10% where she highlighted the week as a red flag and define the number of red flagged week as R.

a. What is a suitable probability distribution for R?

b. Please find the mean and standard deviation of R and interpret the values.

c. What is the probability that more than 40 weeks are being flagged out of the 510 trading weeks?