5. Let f(x) = 3x3/4 and g(x) = -2x314 Find (f + g)(x). Please show work.
1 answer:
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Answer:
(a) The probability that fewer than 3 components will fail is 0.8392.
(b) The mean likely number of failures is 1.44.
Step-by-step explanation:
We are given that a complicated mechanical system contains 8 components. If there is an 18% chance that each component will fail during processing, and components fail independently of each other.
Let X = <u><em>Number of components fail during processing</em></u>
The above situation can be represented through the binomial distribution;
where, n = number of samples (trials) taken = 8 components
r = number of success = fewer than 3 components will fail
p = probability of success which in our question is the probability
that each component will fail during processing, i.e. p = 18%
SO, X ~ Binom(n = 8, p = 0.18)
(a) The probability that fewer than 3 components will fail is given by = P(X < 3)
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
=
=
= <u>0.8392</u>
(b) The mean likely number of failures is given by the following formula;
Mean of X, E(X) = n p
= = 1.44
Hence, the mean likely number of failures is 1.44.