Question

The lifetime of a machine component has a lognormal distribution, given by to​=4472hr and ω =1.26.

a) Determine the probability that a lifetime exceeds 10,000 hours.
b) Determine the lifetime that is exceeded by 90% of machine components

Answer 1

To determine the probability that a lifetime exceeds 10,000 hours and the lifetime that is exceeded by 90% of machine components, we need to use the lognormal distribution.

Step-by-step explanation:

To determine the probability that a lifetime exceeds 10,000 hours, we need to find the area under the right tail of the lognormal distribution curve. Since the mean of the distribution is given by μ = ln(to) + (ω^2 / 2), we can calculate μ and σ using the given values of to​ and ω.

Once we have μ and σ, we can use a cumulative distribution function (CDF) to find the probability.

To determine the lifetime that is exceeded by 90% of machine components, we need to find the value of x such that P(X > x) = 0.90. We can use the inverse of the CDF to find this value.