Question

A lamp has two bulbs, each with an average lifetime of 1600 hours. Assuming that the probability of failure follows an exponential density function with a mean (μ) of 1600, find the probability that both bulbs fail within 1500 hours.

a) 0.2847
b) 0.2153
c) 0.5000
d) 0.7653

Answer 1

To find the probability that both bulbs fail within 1500 hours, use the exponential distribution formula.

Step-by-step explanation:

To find the probability that both bulbs fail within 1500 hours, we can use the exponential distribution formula:

P(x < 1500) = 1 - e-λx

where λ is the decay parameter and x is the time in hours.

Since the mean (μ) of the exponential distribution is equal to 1600, we can calculate the decay parameter (λ) using the formula λ = 1/μ = 1/1600.

Substituting these values into the formula, we get:

P(x < 1500) = 1 - e-(1/1600)(1500)

Calculating this expression gives us the probability that both bulbs fail within 1500 hours.