Question 1174396
**1. Calculate the Standard Error:**

* The standard error of the mean (SEM) measures the variability of the sample mean.
* SEM = σ / √n
    * σ = population standard deviation (250 hours)
    * n = sample size (100 bulbs)
* SEM = 250 / √100 = 250 / 10 = 25 hours

**2. Calculate the z-score:**

* The z-score tells us how many standard errors the sample mean is away from the population mean.
* z = (x̄ - μ) / SEM
    * x̄ = sample mean (1150 hours)
    * μ = population mean (1200 hours)
    * SEM = standard error of the mean (25 hours)
* z = (1150 - 1200) / 25 = -50 / 25 = -2

**3. Find the Probability:**

* We want the probability that the sample mean is greater than 1150 hours. This is the same as finding the area to the right of z = -2 in the standard normal distribution.
* Using a z-table or calculator, look up the probability for z = -2. You'll find a value of approximately 0.0228. 
* Since we want the area to the *right* of z = -2, subtract this value from 1: 1 - 0.0228 = 0.9772

**Therefore, the probability that the sample mean will be greater than 1150 hours is approximately 0.9772.**