Answer:
h;ikl
Step-by-step explanation:
<span>A machine needs 2 of its gears replaced. You find 2 gears, one manufactured 5 years ago and the other manufactured 10 years ago. The specifications sheet says that the chance of failure is 5% after 5 years and increases to 8% after 10 years. If the gears on the machine are in no way linked to each other, what are the chances that both will fail? Answer in % form.
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P(both fail) = 0.05*0.08 = 0.004 = 0.4%</span>
Answer:
u = 4.604 , s = 2.903
u' = 23.025 , s' = 6.49
Step-by-step explanation:
Solution:
- We will use the distribution to calculate mean and standard deviation of random variable X.
- Mean = u = E ( X ) = Sum ( X*p(x) )
u = 1*0.229 + 2*0.113 + 3*0.114 + 4*0.076 + 5*0.052 + 6*0.027 + 7*0.031 + 8*0.358.
u = 4.604
- Standard deviation s = sqrt ( Var ( X ) = sqrt ( E ( X^2) + [E(X)]^2
s = sqrt [ 1*0.229 + 4*0.113 + 9*0.114 + 16*0.076 + 25*0.052 + 36*0.027 + 49*0.031 + 64*0.358 - 4.604^2 ]
s = sqrt ( 8.429184 )
s = 2.903
- We will use properties of E ( X ) and Var ( X ) as follows:
- Mean = u' = E (Rate*X) = Rate*E(X) = $5*u =
u' = $5*4.605
u' = 23.025
- standard deviation = s' = sqrt (Var (Rate*X) ) = sqrt(Rate)*sqrt(Var(X)) = sqrt($5)*s =
s' = sqrt($5)*2.903
u' = 6.49
It would be 120 because 4% of 125 is 5, so you subtract 5 from 125 to get 120. I am pretty sure that's how you do it
