They want to illuminate the squares of the Santiago Centro commune, for this, one known spotlight is installed. The supplier assures that the life time of the bulbs is approximately normal with a mean of 1200 hours and a standard deviation of 150 hours. Choosing one of the bulbs at random, what is the probability that it will shine for at least 980 hours?

Given:
Mean ( \mu ) = 1200 hours
Standard Deviation ( \sigma ) = 150 hours

We need to find the probability that the bulb will shine for at least 980 hours, which means finding P(X \geq 980) .

Using the z-score formula:
z = \frac{X - \mu}{\sigma}
where:
X = 980 hours

Calculating the z-score:
z = \frac{980 - 1200}{150} = \frac{-220}{150} = -1.47

Now, using a standard normal distribution table or calculator, we find the probability that P(Z \geq -1.47) \approx 0.9292 .

Therefore, the probability that the bulb will shine for at least 980 hours is approximately \boxed{0.9292} or 92.92%.

\textbf{Answer:} 0.9292