The lifetime of an LED in a certain application is normally distributed with a mean μ = 25,000 hours and a standard deviation σ = 1500 hours. a. What is the probability that a light bulb will last more than 24,000 hours?

0.7477

Step-by-step explanation:

The mean (X) = 25,000 hrs

Standard deviation (σ) = 1500 hrs

The probability that the light bulb lasts more than 24,000hrs is Pr (X˃24,000)

Using Z-scores, Z = (X - μ) / σ

For X = 24,000

Z = (24,000 - 25,000) / 1500

Z = - 1000/1500

Z = - 0.667

From the normal distribution table, Z = 0.667 = 0.2477

Φ (Z) = 0.2477

Recall that if Z is negative,

Pr (X˃a) = 0.5 + Φ (Z)

Pr (X˃24,000) = 0.5 + 0.2477

= 0.7477