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The time to failure of a component of a mechanical ventilator in weeks has a distribution whose natural logarithm follows a gamma distribution with shape

The time to failure of a component of a mechanical ventilator in weeks has a distribution whose natural logarithm follows a gamma distribution with shape = 1.4 and = 0.2.

a. Calculate the probability that the component fails within 25, 40, and 50 weeks.

b. Calculate the median time to failure.

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