Question

The life in hours of an mri machine is modeled by a weibull distribution with parameters β=0.5 and Δ=500. What is the probability that the mri machine fails between 200 and 250 hours?

Answer 1

To find the probability that the MRI machine fails between 200 and 250 hours, use the Weibull distribution CDF formula with the given parameters.

Step-by-step explanation:

The life in hours of an MRI machine is modeled by a Weibull distribution with parameters β=0.5 and Δ=500.

To find the probability that the MRI machine fails between 200 and 250 hours, we need to calculate the area under the Weibull distribution curve between those two values.

First, we need to find the cumulative distribution function (CDF) for the Weibull distribution. The CDF is given by:

CDF(x) = 1 - exp(-((x/Δ)^β))

Using this formula, we can calculate the CDF for 200 hours and subtract the CDF for 250 hours to find the probability:

Probability = CDF(250) - CDF(200)