Answer to Question #348169 in Statistics and Probability for Abhishek

Question

Q life time of led follow exponential distribution with mean life of 5000 burning hours. if one such LED is selected at random from a big lot, what is the probability that it will last for 

1. at least 4000 hours 

2. almost 10000 hours

Also state the standard deviation of the life time distribution. Given e raised to -0.8 is 0.4493 and e raised to -2 is 0.1353

Answer 1

$$\lambda=1/\mu=1/5000=0.0002$$

1.

$$P(X\ge4000)=e^{-0.0002(4000)}=e^{-0.8}\approx0.449329$$

2.

$$P(X\le10000)=1-e^{-0.0002(10000)}=1-e^{-2}\approx0.864665$$

The standard deviation is always equal to the mean: $\sigma=\mu=5000h.$