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

To find the specification limit such that only 0.5% of the bulbs will not exceed this limit we proceed as follows;

From the z-table, a z-score of - 2.57 cuts off 0.005 in the left tail; given the formula for z-score

(x-μ) / σ

we shall have:

(x-5000) / 50=-2.57

solving for x we get:

x-5000=-128.5

x=-128.5+5000

x=4871.50