Question

From past, a company knows that in cartons of bulbs, 90% contain no defective bulbs, 5%

contain one defective bulb, 3% contain two defective bulbs, and 2% contain three defective
bulbs. Find the mean and standard deviation for the number of defective bulbs. ​

Answer 1

The mean is M=0.17 defective bulbs.

The standard deviation is s=0.165 defective bulbs.

Explanation:

We can calculate the mean as the sum of the product between the number of defective bulbs and its proportion:

`M=\sum_i p_i\cdot X_i=0.9\cdot0+0.05\cdot 1+0.03\cdot2+0.02\cdot3\\\\M=0+0.05+0.06+0.06\\\\M=0.17`

The standard deviation can be calculated as the sum of the product between the deviation from the mean for each number of defective bulbs and its proportion:

`s=√(\sum_i p_i\cdot (X_i-M)^2)\\\\s=√(0.9\cdot(0-0.17)^2+0.05\cdot (1-0.17)^2+0.03\cdot(2-0.17)^2+0.02\cdot(3-0.17)2)\\\\s=√(0.02601+0.00072+0.000363+0.000242)\\\\s=√(0.027335)\\\\s\approx0.165`