Question

An average light bulb manufactured by the Acme Corporation lasts 300 days with a standard deviation of 50 days.


Assuming that bulb life is normally distributed, what is the probability that an Acme light bulb will last at most 365 days?

Answer 1

First you have to calculate the z-score.

You can find the z-score by taking the value you are interested in (365), subtracting the mean (300), and then dividing this sum by the standard deviation (50). You should get z=1.3. This means that your value lies 1.3 standard deviations to the right of the mean. You're looking for the right tail of this curve.

Look up z=1.3 on a z-table. Make sure the right side is shaded. If the left tail is shaded on the diagram, then you need to look at z=-1.3 for the correct percentage.