SOLUTION: Suppose that for single launches of a space shuttle, there is a constant probability of O-ring failure (say, .15). Consider ten future launches, and let X be the number of those in

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Question 1092450: Suppose that for single launches of a space shuttle, there is a constant probability of O-ring failure (say, .15). Consider ten future launches, and let X be the number of those involving an O-ring failure. Use an appropriate probability model and evaluate all of the following:
a) P[x=2]
b) P[x>=1]
c) EX
d) Var X
e) standard deviation of X=
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
Use the binomial probability formula
:
Probability (P) (k events in n trials) = nCk * p^k * (1-p)^(n-k) where p is probability of event occurring, nCk = n! / (k! * (n-k)!)
:
p = 0.15, n = 10
:
a) P(x=2) = 10C2 * (0.15)^2 * (1-0.15)^(10-2) = 0.276 approximately 0.28
:
b) P(x>=1) = 1 - P(x=0) = 1 - 0.20 = 0.80
:
c) I assume by EX you mean E(X)
E(X) = np = 10 ^ 0.15 = 1.5
:
d) Var(X) = np(1−p) = 10 * (0.15) * (1-0.15) = 1.275
:
e) standard deviation of X = square root(1.275) = 1.1292
: