The average time between accidents in a factory is 14 weeks. Find the probability that more than 17 weeks pass between accidents.

Answer 1

Salma, great question!

Given Data: Average time between accidents is 14 weeks.

Objective: Find the probability that more than 17 weeks pass between accidents.

Assumptions:

1. The time between accidents follows an exponential distribution.
2. Accidents occur independently.
3. The rate is constant over time.

Formula and Calculations:

1. Rate parameter (lambda) is 1/14.
2. Cumulative Distribution Function (CDF) for 17 weeks is 1 - e^(-1/14 * 17).
3. Probability that more than 17 weeks pass is 1 - CDF for 17 weeks.

Result: The probability that more than 17 weeks will pass between accidents is approximately 0.297 or 29.7%.

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Best regards,

Ben