In my previous post<\/a> I gave the premise of a part whose mean life (\u03bc) is 36 months, with standard deviation (\u03c3) 10 months. I went on to give a one-sided 95% confidence interval for its minimum life expectancy.<\/p>\n Today, I’ll give a two-sided 95% confidence interval for the part’s expected life. From the normal distribution table, we see that 97.5% of the distribution is less than In our case, \u03bc=36, while \u03c3=10. The two-sided interval is 36-1.96(10) to 36+1.96(10), or 16.4 to 55.6 months. 95% of the time, the part will last between 16.4 months and 55.6 months.<\/p>\n Compared to the one-sided interval of the previous post (which was \u226519.55), the two-sided interval is more permissive on the low end (at 16.4). However, it’s less permissive on the top end (55.6); the one-sided interval makes no estimate of top end life.<\/p>\n I’ll be talking more about confidence intervals.<\/p>\n Source:<\/p>\n Harnett, Donald L. and James L. Murphy. Statistical Analysis for Business and
\n\u03bc + 1.96\u03c3. By symmetry, 97.5% will also be greater than \u03bc – 1.96\u03c3. Therefore, the interval from \u03bc – 1.96\u03c3 to \u03bc + 1.96\u03c3 covers the middle 95% of the distribution, since it excludes both the top and bottom 2.5%.<\/p>\n
Economics<\/em>. Don Mills: Addison-Wesley, 1993.<\/p>\n