A lightbulb has a normally distributed light output with mea

A lightbulb has a normally distributed light output with mean 5000 end foot-candles and standard deviation of 50 end foot-candles. Find a lower specification limit such that only 0.5% of the bulbs will not exceed this limit. Can someone explain to me in detail this include how the cumulative standard normal distribution table is incorporated?

Solution

The first thing to do is to consult a table for the standard normal distribution, to find out a number that only 0.5% = 0.0050 of observations are below. According to my table, a number of -2.58 returns a probability of 0.0050. This means that only 0.0050 = 0.5% of observations are more than 2.58 standard deviations below the mean.

How much is 2.58 standard deviations, in this problem? Each standard deviation is 50. 2.58 standard deviations is 2.58*50 = 159. \"2.58 standard deviations below the mean\" is then 5000 - 159 = 4871. Only 0.5% of lightbulbs will produce less than 4871 end foot-candles (whatever those are?).

I hope this helps!