Question

Suppose that the lifetimes of a certain kind of light bulb are normally distributed with a standard deviation if 110 hours. If exactly 95% of the bulbs die before 920 hours, find the mean lifetime if the bulbs

Answer 1

The mean life time of the bulbs is approximately 739 hours

Explanation:

Here, we want to calculate the mean life time

From the question, 95% of the bulbs die before 920 hours

What this mean is that the probability that a bulb will die before 920 hours is 95% = 95/100 = 0.95

Now, we need the z-score that is exactly equal to this value

Using the standard normal distribution table, the z-score corresponding to this probability value is 1.645

Mathematically;

z-score = (x-mean)/SD

In this case, x is 920, SD is standard deviation which is 920 hours

thus, we have it that;

1.645 = (920-mean)/110

110(1.645) = 920 - mean

180.95 = 920 - mean

mean = 920- 180.95

mean = 739.05