Answer:
The right answer is:
(a) -10.67
(b) 0.7986
Step-by-step explanation:
(a)
According to the question,
<u>X P(X) X.P(X) X2.P(X)</u>
<u>12130 0.002 24.26 294274</u>
<u>-35 0.998 -34.93 1222.55</u>
Now,
![\Sigma x.P(x) = -10.67](https://tex.z-dn.net/?f=%5CSigma%20x.P%28x%29%20%3D%20-10.67)
or,
![\Sigma x^2.P(x) = 295496.35](https://tex.z-dn.net/?f=%5CSigma%20x%5E2.P%28x%29%20%3D%20295496.35)
hence,
The mean will be:
![\Sigma x.P(x) = -10.67](https://tex.z-dn.net/?f=%5CSigma%20x.P%28x%29%20%3D%20-10.67)
(b)
According to the question,
n = 12
p = 0.125
q = 1 - p
= 0.875
Now,
⇒ ![P(X=x) = \binom{n}{x} p^x q^{n-x}](https://tex.z-dn.net/?f=P%28X%3Dx%29%20%3D%20%5Cbinom%7Bn%7D%7Bx%7D%20p%5Ex%20q%5E%7Bn-x%7D)
By substituting the values, we get
⇒ ![P(X \geq 1)=1-(\binom{12}{0} 0.125^0. 0.875^{12-0})](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%201%29%3D1-%28%5Cbinom%7B12%7D%7B0%7D%200.125%5E0.%200.875%5E%7B12-0%7D%29)
⇒ ![=1-(1 (0.125^0) (0.875^{12}))](https://tex.z-dn.net/?f=%3D1-%281%20%280.125%5E0%29%20%280.875%5E%7B12%7D%29%29)
⇒ ![=1-(1(1.0)(0.2014))](https://tex.z-dn.net/?f=%3D1-%281%281.0%29%280.2014%29%29)
⇒ ![=1-(0.2014)](https://tex.z-dn.net/?f=%3D1-%280.2014%29)
⇒
Im not really good at these but i do think it is c. Sorry im not 100% sure. <span />
Answer:5.4 km
Step-by-step explanation: