A day trading firm closely monitors and evaluates the
performance of its traders. For each $10,000 invested, the daily
returns of traders at this company can be modeled by a Normal
distribution with mean = $901 and standard deviation = $2,722.
(a) What is the probability of obtaining a negative daily
return, on any given day? (Use 3 decimals.)
(b) Assuming the returns on successive days are independent of
each other, what is the probability of having a negative daily
return for two days in a row? (Use 3 decimals.)
(c) Give the boundaries of the interval containing the middle
80% of daily returns: (use 3 decimals) ( , )
(d) As part of its incentive program, any trader who obtains a
daily return in the top 2% of historical returns receives a special
bonus. What daily return is needed to get this bonus? (Use 3
decimals.)