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: email@example.com
Hosting provided by Zymic.
For acknowledgments related to CSS and other code used, click here.
Linked or embedded works (software, books, articles, etc.) are presented under their own licenses.
Other unique content on this page, excluding screenshots, is distributed under the following license: C.C. Attribution NonCommercial ShareAlike 3.0. In some cases, screenshots are distributed under the same license. In other cases, the associated program's license applies.
Valid XHTML 1.0