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For X ~ BIN(20, 0.6), find the following probabilities (PLEASE SHOW CLEAR WORK): P(X = 14)...

For X ~ BIN(20, 0.6), find the following probabilities (PLEASE SHOW CLEAR WORK):

P(X = 14) =

P(X > 15) =

P(X < 9) =

Expert Solution

We have given ,

For X ~ BIN(20, 0.6),

P(X = 14) =C(20,14)*(0.6)^14*(1-0.6)^6

= 0.1244

or by using Excel command =BINOMDIST(14,20,0.6,FALSE) = 0.1244

P(X > 15) =P[X=16] + P[X=17] + P[X=18] + P[X=19] + P[X=20]

=0.035+0.0123+0.0031+0.0005+0..............by using calculated probabilities from below table

= 0.0509

by using Excel

= 1-0.9490 .........................................by using =BINOMDIST(15,20,0.6,TRUE)

=0.051

P(X < 9) =P[X=0] + P[X=1] + P[X=2] + P[X=3] +P[X=4] +P[X=5]+P[X=6]+P[X=7]+P[X=8]

=0+0+0+0+0.0003+0.0013+0.0049+0.0146+0.0355.................by using calculated probabilities from below table

=0.0566

by using Excel.

= 0.0566............................by using =BINOMDIST(8,20,0.6,TRUE)

By using formula C(n,r) (p)^r*(1-p)^n-r where n = 20 , p = 0.6 , x= 0 , 1 , 2 , ..........................20

x	Pr[X = x]
0	0
1	0
2	0
3	0
4	0.0003
5	0.0013
6	0.0049
7	0.0146
8	0.0355
9	0.071
10	0.1171
11	0.1597
12	0.1797
13	0.1659
14	0.1244
15	0.0746
16	0.035
17	0.0123
18	0.0031
19	0.0005
20	0

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