Reference no: EM132413563

(a) Robinhood is a trading App with no commissions or fees. The company has reported an average number of daily active users (DAU) of 53,000, with a standard deviation of 60,000. An analyst is analyzing data for the past 400 days. What is the probability that the sample mean of DAU is larger than 50,000?

(b) A Robinhood user is considered "active" if s/he executes at least one trade per day. However, there are many users that trade at a lower frequency. 30% of users have invested more than $10,000. If a user has invested at least $10,000, the probability that s/he is active is 15%. On the other hand, if a user has invested less than $10,000, the probability that s/he is active is 23%. Given that a user is active, what is the probability that s/he invested more than $10,000?

(c) A sizeable proportion of Robinhood users seem to be day-traders (i.e., speculators in volatile stocks that close their positions at the end of every trading day). Robinhood estimates that at the end of the day, the return on $1 invested in day-trading is normally distributed. Robinhood's trading records suggest that, on average, $1 invested in day-trading is worth only 95 cents at the end of the day (i.e., day-traders lose money as a group even though there might be some individual day-traders who make a fortune). The records also suggest a 16% chance that a $1 day-trading investment will turn out to be profitable at the end of the day. Using Robinhood's records and estimates, find the standard deviation of the return at the end of the day on $1 invested in day-trading.