Question

The service life of lightbulbs in the rooms of Swenson hall is on average 4000 hours with a standard deviation of 250 hours. Once 30 bulbs die, they replace all the bulbs in the building for precaution. How likely is it the average lifespan of those 30 bulbs is less than 4100 hours after they are all installed?I want answer and explanation.

Answer 1

Step-by-step explanation:

Let us assume that the service life of lightbulbs in the rooms of Swenson hall are normally distributed. Let x be a random variable representing the average lifespan of the lightbulbs.

We would calculate the z score by applying the formula,

z = (x - μ)/(σ/√n)

where

x is the sample mean

σ is the population standard deviation

μ is the population mean

n is the sample size

From the information given,

σ = 250

μ = 4000

n = 30

x = 4100

By substituting these values into the formula,

z = (4100 - 4000)/(250/√30) = 2.19

We want to find P(x < 4100). From the normal distribution table, the probability value for a z score of 2.19 is 0.9857

Thus, the probability that the average lifespan of those 30 bulbs is less than 4100 hours after they are all installed is 0.9857