a monitor has an average life span of 15,000 hrs & a standard deviation of 2000 hrs, prob life span is -15000?

Question

this is a statistics problem, the end should say what is the probability the life span is less than 15,000 hours

Answer 1

Since the life-span is a MEAN Time Before Failure, and the distrubution is Gaussian, 1/2 of the units will fail before 15,000 hours. Most of that "half" will fail close to 15,000 hours, but statistically 1/2 of them will fail before 15,000 hours.

Give me a specific time (i.e. 10,000 hours) and I can tell you how many (statistically) will fail at or before that time.

.

Answer 2

Is this a trick question?

If you use the normal distribution, and you take the average(mean) to be 15,000 and thus the centre of the distribution... the probability that the life span is less than 15,000 hours is just half of the area under the probability distribution curve (the left area)

Probability = 0.5

Answer 3

Because you mentioned that the two parameters are mean and standard deviation, I'm assuming that the failure distribution is normal, although usually electronic devices fail according to exponential or Weibull distributions. Anyway,

Z = (x - µ)/σ = (15000 - 15000)/2000 = 0
The standard normal table of probabilities, for Z = 0, gives a probability of 0.50 of failing before 50000 hours.