Final answer:
The probability that the bulb will last less than 1,250 hours is 71.35%.
Step-by-step explanation:
To calculate the probability that the bulb will last less than 1,250 hours, we need to use the exponential distribution formula. In this case, the mean (mu) of the exponential distribution is 1,000 hours. The probability (P) that the bulb will last less than a given number of hours (x) can be calculated using the formula P(x) = 1 - e^(-x/mu), where e is the base of the natural logarithm.
Plugging in the values, we have P(1250) = 1 - e^(-1250/1000). Using a calculator, we find that P(1250) is approximately 0.7135 or 71.35%. Therefore, the probability that the bulb will last less than 1,250 hours is 71.35%, which corresponds to answer choice a.