Question

please solve this problem using excel and show steps please

D. and the standard deviation of this distribution. 71. FILE Refer to the Baseball 2016 data. Compute the mean number of home runs per game. To do this, first find the mean number of home runs per team for 2016. Next, divide this value by 162 (a season comprises 162 games). Then multiply by 2 because there are two teams in each game. Use the Poisson distribution to estimate the number of home runs that will be hit in a game. Find the probability that: a. There are no home runs in a game. b. There are two home runs in a game. C. There are at least four home runs in a game.

Answer 1

1. Put the data in excel and find the mean as shown. Divde the mean by 162 and multiply by 2. Also the method to solve in excel is shown

Hence the mean home run per games is 2.03

А. B с D E F G H 1 HR 2 3 Total of the HR No. of games HR per game HR per team 164 =AVERAGE(A2:A31) 162 1.01008 =E2/E3 2.02016 =E4*2 4 5 LC 7 a. There are no home runs in a game P(X=0) 0.13264 =POISSON.DIST(0,2.0201, FALSE) 8 b. There are two home run in the games PIX=1) 0.26795 =POISSON.DIST(1,2.0201,FALSE) 154 100 217 161 171 136 167 141 186 151 230 139 176 187 120 145 156 177 212 146 130 140 148 136 198 137 167 172 ཀ བན 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 C. There are at least four home runs in a game. PlX >=4) = 1 - PIX = 0) + PIX = 1) + P(X = 2) + P(X = 3)) P(X=0) P(X=1) P(X=2) P(X=3) 0.13264 =POISSON.DIST(0,2.0201, FALSE) 0.26795 =POISSON.DIST(1,2.0201,FALSE) 0.27064 =POISSON.DIST(2,2.0201, FALSE) 0.18224 =POISSON.DIST(3,2.0201,FALSE) P(X >=4) 0.14652 =1-(SUM(E18:E21))

Let x denote the number of homes in a game. Here the random variable x follows a poisson distribution and with parameter mean = 2.03.

e P(X = x) !

a. There are no home runs in a game

We need to find P(X=0)

zły a P(X = 0) = (e-2.0201) (2.02019) 0! II =0.1326 x!

b. There are two home run in the games

We need to find P(X=2)

-2.0201)(2.02012) II P(X = 2) = e la -=0.2706 ! 2!

C. There are at least four home runs in a game.

We need to find P(X>=4)

P(X >=4) = 1 -( P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3))

P(X = 0) = (e-2.0201) (2.02019) -=0.1326 zł, a = x! 0! alpa -2.0201) (2.02011) P(X = 1) = 11 -=0.268 r! 1! alpa -2.0201) (2.0201²) II P(X = 2) = =0.2706 ! 2! alpa (e-2.0201)(2.0201) -=0.1822 P(X = 3) = II ! 3!

P(X >=4) = 1 -( 0.1326 +0.268 + 0.2706 + 0.1822 ) = 0.1466