Answer to Question #297362 in Statistics and Probability for Lian

Question

The lifetime of a light bulb is normally distributed with 800 hours and standard deviation 50 hours. A random light bulb is selected. What is the probability that it will last for more than 950 hours?

Answer 1

$P(x > 950) = P\left( {950 < x < \infty } \right) = \Phi \left( \infty \right) - \Phi \left( {\frac{{\alpha - a}}{\sigma }} \right) = \Phi \left( \infty \right) - \Phi \left( {\frac{{950 - 800}}{{50}}} \right) = \Phi \left( \infty \right) - \Phi \left( 3 \right) = 0.5 - 0.4987 = {\rm{0}}{\rm{.0013}}$

Answer:0.0013