Answer:
a) P(X =16 ) = 0.1853
b) [tex]P(X \leq 12)[/tex] = 0.0684
Step-by-step explanation:
GIVEN DATA:
n = 16
p = 0.90
from relation given probabllity can be solve
[tex]P(X) = ^nC_x * p^x * ( 1 - p)^{n-x}[/tex]
a)
[tex]P(X =16 ) = ^{16}C_{16} * 0.90^x * ( 1 - 0.90)^{16-16}[/tex]
P(X =16 ) = 0.1853
b) [tex]P(X \leq 12) = 1 - P(X \geq 13)[/tex]
= 1 - [ P(X = 13) +P(X = 14) +P(X = 15) +P(X = 16) ]
[tex]= 1 - [ ^{16}C_{13} * 0.90^{13} * (1 - 0.90)^3 +^{16}C_{14} * 0.90^{14} * (1 - 0.90)^2 +^{16}C_{15} * 0.90^{15} * (1 - 0.90)^1 +^{16}C_{16} * 0.90^{16} * (1 - 0.90)^0 ][/tex]
= 0.0684
