Question

The local authorities in a certain city install 10,000 electric lamps in the streets of the city. If these lamps have an average life of 1000 burning hours with a standard deviation of 200 hours, assuming normal distribution, what number of lights might expected to fail :

In the first 800 burning hours         

After how many burning hours 10% of the lamps would be still burning?

                                                                                

Answer 1

Solution: It is given:

Let x be the random variable that denotes the number of hours the lamp lights up.

what number of lights might expected to fail in the first 800 burning hours

Answer: We are required to find the expected number of lights to fail in the first 800 burning hours.

First, we have to find the probability as:

Using the z-score formula, we have:

  

Now using the standard normal table, we have:

Therefore, the expected number of lights to fail in the first 800 burning hours is:

After how many burning hours 10% of the lamps would be still burning?

Answer: We first need to find the z-value corresponding to area = 1- 0.10 = 0.90. Using the standard normal table, we have:

Now using the z-score formula, we have: