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Mathematics

1 answer:

Stolb23 [73]3 years ago

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Answer: the answer is 76 please give me brainliest im trying to rank up.

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A complicated mechanical system contains 8 components. If there is a 18% chance that each component will fail during processing,

kicyunya [14]

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 = Number of components fail during processing

The above situation can be represented through the binomial distribution;

$P(X=r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ;x=0,1,2,.....$

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)

= $\binom{8}{0}\times 0.18^{0} \times (1-0.18)^{8-0}+ \binom{8}{1}\times 0.18^{1} \times (1-0.18)^{8-1}+ \binom{8}{2}\times 0.18^{2} \times (1-0.18)^{8-2}$