Question: An Internet based trading service, Speculate.com, estimates that at the end of the day the return on $1 invested in day-trading is normally distributed. Speculate.com's

An Internet based trading service, 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 95c 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.

a)Find the standard deviation of the return at the end of the day on $1 invested in day-trading.

b) Some analysts do not completely agree with the estimates provided by Speculate.com. While they do agree that at the end of the day the return on $1 invested in day-trading is normally distributed, they believe that, on average, it will be worth only 90c with a standard deviation of 20c. Using the analysts' estimates, find the probability that $1 invested in day-trading will be worth more than $1.25 at the end of the day.

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