Interpret the key results for Inverse Cumulative Distribution Function (ICDF)

The inverse cumulative distribution function (ICDF) provides the x-value for a specific cumulative probability.

For a continuous distribution, Minitab calculates the x-values for each cumulative probability that you specify.

Inverse of the Cumulative Probability
P(X ≤ x)
x
Key Results: P(X ≤ x) and x for a continuous distribution

In these results, the time by which 5% of the heating elements are expected to fail is the ICDF of 0.05, or 507 hours. The time at which only 5% of the heating elements are expected to continue to function is the ICDF of 0.95, or 1493 hours. The times between which 95% of all heating elements are expected to fail is the ICDF of 0.025 and the ICDF of 0.975, or between 412 hours and 1588 hours.

For a discrete distribution, there may not be an exact x-value for the cumulative probability that you specify. Therefore, Minitab displays exact integer values for the cumulative probabilities that are closest to your desired cumulative probability.

Inverse of the Cumulative Probability
x
P(X ≤ x)
x
P(X ≤ x)
Key Results: P(X ≤ x) and x for a discrete distribution

In these results, the x-values are given for a binomial distribution with 100 trials and event probability of 0.03. For example, suppose you want to know the number of defectives that are associated with a cumulative probability of 50%. The cumulative probability is 0.419775 at x = 2 and the cumulative probability is 0.647249 at x = 3. The binomial distribution is a discrete distribution that cannot take x-values between 2 and 3, so there is no x-value associated with the exact cumulative probability of 0.50.

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