Speculate.com is an internet trading company. The company is worried about the continual market slide; it seems to have resulted in a significant decline in both the total number of trades Speculate.com executes and the number of customers who actively trade on Speculate.com.
A sizeable proportion of Speculate.com customers seem to be day-traders (i.e., speculators in volatile stocks that close their positions at the end of every trading day). Speculate.com estimates that at the end of the day, the return on $1 invested in day-trading is normally distributed. Speculate.com’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 45% chance that a $1 day-trading investment will turn out profitable at the end of the day. Using Speculate.com’s records and estimates, find the standard deviation of the return at the end of the day on $1 invested in day-trading.