# The local authorities in a cer

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

In the first 800 burning hours

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

Solution: It is given:

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

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

Answer: We are required to find the expected number of lights tofail 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 first800 burning hours is:

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

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:

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