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Roulette If you place a bet on the number 7 in roulette, you have a 1/38 probabi

ID: 3250189 • Letter: R

Question

Roulette If you place a bet on the number 7 in roulette, you have a 1/38 probability of winning. a. Find the mean and standard deviation for the number of wins for people who bet on the number 7 fifty times. b. Would 0 wins in 50 bets be an unusually low number of wins? Born on the 4th of July For the following questions, ignore leap years. a. For classes of 30 students, find the mean and standard deviation for the number born on the 4th of July. Express results using seven decimal places. b. For a class of 30 students, would 2 be an unusually high number who were born on the 4th of July? Powerball Lottery As of this writing, the Powerball lottery is mn in 42 states. If you buy one ticket, the probability of winning is 1/195, 249, 054. If you buy one ticket each week for 50 years, you play this lottery 2600 times. a. Find the mean and standard deviation for the number of wins for people who buy a ticket each week for 50 years. Express the results using six decimal places. b. Would it be unusual for someone to win this lottery at least once if they buy a tick week for 50 years?

Explanation / Answer

18)

probability of winning i.e p = 1/38

no of bets or trails i.e n = 50

mean = np = 50*(1/38) = 1.3158

variance = np(1-p) = 50*(1/38)(1-1/38) = 1.2812

standard deviation = varinace = 1.2812 = 1.1319

b)

Probabilty of 0 wins in 50 bets = (1-1/38)50 = 0.2636

event is unusual if its probability is less than 0.05

Probability 0 wins is 0.2636>0.05 which is not unusual

19)

Probabity of being born on 4th july i.e p= 1/365

no of students i.e n = 30

mean = np = 30*(1/365) = 0.0822

variance = np(1-p) = 30*(1/365)(1-1/365) = 0.082

standard deviation = varinace = 0.082 = 0.2864

b)

probabity tha atleast 2 students are born on july 4th = 1- P(0)-P(1)

= 1- (364/365)30- 30*(1/365)*(364/365)29 = 0.003

event is unusual if its probability is less than 0.05

so 2 is unusulally high number number who were born on july 4th