Answer :
Final answer:
The probability that the component will fail within 13 hours is approximately 0.6827.
Explanation:
To find the probability that the component will fail within 13 hours, we can use the cumulative distribution function (CDF) of the Weibull distribution. The CDF gives us the probability that the failure time is less than or equal to a given value.
The CDF of the Weibull distribution is given by:
F(x) = 1 - exp(-(x/b)^a)
where x is the failure time, a is the shape parameter, and b is the scale parameter.
Substituting the given values, a = 2.06 and b = 1.18, and x = 13, we can calculate the probability as follows:
F(13) = 1 - exp(-((13/1.18)^2.06))
Using a calculator, we find that F(13) ≈ 0.6827.
Learn more about probability of failure within a given time using weibull distribution here:
https://brainly.com/question/30430742
#SPJ11