Question

Suppose that lifetimes of light bulbs produced by a certain company are uniformly distributed between 700 and 1100 hours. What is the probability for a randomly selected 64 light bulbs that total lifetime is at least 55600 hours? (use 4 digits after decimal point)  [hint: P(ΣX ≥ 55600 hours)=?]

Answer 1

Let X be a random variable that denotes the lifetime of a single bulb.

Given that lifetimes of a single bulb is uniformly distributed between 700 hours and 1100 hours. This gives the mean and variance of the lifetimes of a single bulb as:

Assuming that the lifetimes of the bulbs are independent of each other and using the central limit theorem the total lifetimes of 64 bulbs follows a normal distribution with parameters:

Thus, the probability for a randomly selected 64 light bulbs the total lifetime is at least 55600 hours is

Thus the required probability is 0.98461.