SOLUTION: An electrical company claims that the average life of the bulbs it manufactures is 1200 hours within a standard deviation of 250 hours. If a random sample of 100 bulbs is chosen, w

Question 1174396: An electrical company claims that the average life of the bulbs it manufactures is 1200 hours within a standard deviation of 250 hours. If a random sample of 100 bulbs is chosen, what is the probability that the sample mean will be greater than 1150 hours
Answer by CPhill(1987) (Show Source): You can put this solution on YOUR website!
**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.**
RELATED QUESTIONS
3.An electrical company claims that the average life of the bulbs it manufactures is 1200 (answered by ikleyn)

A company manufactures light bulbs and wants to advertise a me an life of 1200 hours for... (answered by ewatrrr)

"An electrical firm manufactures light bulbs that have a length of life that is... (answered by CPhill)

. An electrical firm manufactures light bulbs that have a length of life that is normally (answered by stanbon)

Please help me. t distribution related problem. Acme corporation manufactures light... (answered by Positive_EV)

A light bulb company claims that the 40 watt light bulb it sells has an average life of... (answered by Theo)

1. Liwanag Bulb Company claims that it sells light bulbs with an average life of 1000... (answered by Theo)

A light-bulb manufacturer claims that the light bulbs produced by his company have an... (answered by stanbon)

An electrical firm manufactures incandescent light bulbs that have a length of life (in... (answered by Theo)