Question

Based on past results found in the Information Please Almanac, there is a 0.1919 probability that a baseball World Series contest will last four games, a 0.2121 probability that it will last five games, a 0.2222 probability that it will last six games, and a 0.3737 probability that it will last seven games. (a) Clearly describe both reasons why this is a valid probability function? (b) Find the mean and standard, variance and deviation (with proper units) for the number of games in World Series contests and interpret the mean. (c) Is it unusual for a team to "sweep" by winning in four games? Why or Why not? ( Use the z-score method)

Answer 1

as sum of probability is 1 and individual probability are within range of 0 to 1 ;

therefre it is a valid probability distribution

b)

x	p(x)		xP(x)	x2P(x)	(x-μ)2		(x-μ)2P(x)
4	0.1919		0.768	3.070	3.158		0.606
5	0.2121		1.061	5.303	0.604		0.128
6	0.2222		1.333	7.999	0.050		0.011
7	0.3737		2.616	18.311	1.495		0.559
total	0.9999	μ=	5.78	34.683	5.307	σ2=	1.3040
					std deviation=     σ =    √σ2 =		1.1419

here mean =5.78 varaince =1.3040 and std deviation =1.1419

whcih reflect that on average for a number of series  expected number of games lasted by a team is 5.78 with in error of 1.1419 games/.

c)as probability of that happening is not less than 0.05 levl of significance therefore it is not unusual