# Light-bulb lifetime puzzle

Q. I'm studying statistics. A website had a problem similar to this one:

Assume that a typical light bulb manufactured by the Acme Corporation lasts 300 days and that the standard deviation is 50 days. Bulb life follows a normal distribution. What is the probability that a light bulb made by this company will last at most 365 days?

My answer is shown below. It's different from what the website said. Check my answer.

x=365 m=300 r=50 and I got 0.8485

A. Your answer seems to be incorrect. The correct answer is 0.9032 (or 90.32%, written as a percentage). I'll show you how to get this result below.

This light-bulb puzzle is a standard example that is common on the Web. They expect you to use a z-score to find the answer. For an explanation of z-score, click here.

To compute a z-score in problems of this nature, take a value on the x-axis (or characteristic that is being plotted as a Bell Curve), subtract the mean (or most typical value), and divide by the standard deviation. In this case, the result is (365 days minus 300 days) divided by 50 days; or 1.30.

You can take a z-score and look it up in a z-score table of the appropriate type to determine the fraction of the total area under the Bell Curve that is located to the left of the x-value that is used. In the current example, the area in question gives the probability that is being sought.

As of May 2012, there was a z-score table of the appropriate type located at this link. For a z-score of 1.30, the result was 0.9032. Written as a percentage, this is 90.32%.

If people notice mistakes in my reasoning, please send corrections to me at: oldcoder@yahoo.com

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