Statistics Question

Question

Many electronics follow a failure rate described by an exponential probability density function (PDF). Solar panels are advertised to last 20 years or longer, but panels made in China are failing at a higher rate. The time-to-failure of this device is usually exponentially distributed with mean 6 years. 

What is the probability of failure in the first 8 years? 

Answer 1

Hi Kristen! I'm glad to assist here. First, assess the inputs, then plug the values into the formula 1 − e^(-rate × time), and calculate!

Step 1: Identify the Given Values and Formula

1. Mean: 6 years
2. Rate parameter: 1 ÷ Mean = 1 ÷ 6
3. Time: 8 years
4. Formula: Probability = 1 − e^(-rate × time)

Step 2: Plug the Values into the Formula

1. Calculation: 1 − e^-(8 ÷ 6) = 1 − e^-(4 ÷ 3)

Step 3: Calculate the Probability

1. Calculation: 1 − e^-1.3333 = 1 − 0.2636 = 0.7364

The probability that a panel fails in the first 8 years is 0.7364 (or 73.64%).