Question

In the 2004 baseball season, Ichiro Suzuki of the Seattle Mariners set the record for most hits in a season with a total of 262 hits. In the following probability distribution, the random variable X represents the number of hits Ichiro obtained in a game.

X	0	1	2	3	4	5
P(X)	0.1677	0.3354	0.2857	0.1491	0.0373	0.0248

1. What is the probability that in a randomly selected game, Ichiro got at least 3 hits? =.2112
2. Compute the mean of the random variable X. (round to two decimal places) =1.63
3. Compute the standard variation of the random variable X. (round to two decimal places) =1.18

4) What would be the upper limit of range that would include the number of hits Ichiro obtained in 75% of the games?

Answer 1

we have given

X	0	1	2	3	4	5
P(X)	0.1677	0.3354	0.2857	0.1491	0.0373	0.0248

X	0	1	2	3	4	5	Total
P(X)	0.1677	0.3354	0.2857	0.1491	0.0373	0.0248	1
XP(X)	0	0.3354	0.5714	0.4473	0.1492	0.124	1.6273
X^2P(X)	0	0.3354	1.1428	1.3419	0.5968	0.62	4.0369

1 ) the probability that in a randomly selected game, Ichiro got at least 3 hits is P(X =3) +P(X=4) +P(X =5) = 0.1491+0.0373+0.0248 = .2112

2 ) the mean of the random variable E(X ) = = 0*0.1677+1*0.3354+2*0.2857+3*0.1491+4*0.0373+5*0.0248 =1.6273 ~1.63

3 )E(X2) = =0*0*0.1677+1*1*0.3354+2*2*0.2857+3*3*0.1491+4*4*0.0373+5*5*0.0248 = 4.0369

standard variation of the random variable X =

= = 1.18