If you play roulettes and bet on 'red' the probability that you win is 18/38 = .4737. People often repeat this between several times. We can consider each time we play a 'trial' and consider it a success when we win, so p = 18/38 or (.4737) and q = 20/38   or (.5263). Suppose that Caryl always places the same bet when she plays roulette, $5 on 'red'. Caryl might play just once, or might play several times. She has a profit (having won $5 more times than she lost $5) if she wins more than half of the games she plays.   -when you play 401 times, p is the proportion of those 401 games that you win. You'll profit (winning more than you lose) if you win more than half of your bets p > .5000.     c) what is the mean or expected value of p? d) what is the standard deviation of p? e) assume that the distribution of p is Normal and find the probability that Caryl will have a profit if she plays 401 times. show your work or calculator input and round your answer to four decimal places

If you play roulettes and bet on 'red' the probability that you win is 18/38 = .4737. People often repeat this between several times. We can consider each time we play a 'trial' and consider it a success when we win, so p = 18/38 or (.4737) and q = 20/38   or (.5263).

Suppose that Caryl always places the same bet when she plays roulette, $5 on 'red'. Caryl might play just once, or might play several times. She has a profit (having won $5 more times than she lost $5) if she wins more than half of the games she plays.

-when you play 401 times, p is the proportion of those 401 games that you win. You'll profit (winning more than you lose) if you win more than half of your bets p > .5000.

c) what is the mean or expected value of p?

d) what is the standard deviation of p?

e) assume that the distribution of p is Normal and find the probability that Caryl will have a profit if she plays 401 times. show your work or calculator input and round your answer to four decimal places