Answer to Question #265389 in Statistics and Probability for nunu

Question

The lifetimes of lightbulbs that are advertised to last for 5,000 hours are normally distributed with a mean of 5,100 hours and a standard deviation of 200 hours. What is the probability that a bulb lasts longer than the advertised figure?

Answer 1

$X\sim N(\mu, \sigma^2)$

Given $\mu=5100, \sigma=200$

$$P(X>5000)=1-P(X\leq5000)$$

$$=1-P(Z\leq\dfrac{5000-5100}{200})$$

$$=1-P(Z\leq-0.5)$$

$$\approx0.691462$$