Answer:
The mean is M=0.17 defective bulbs.
The standard deviation is s=0.165 defective bulbs.
Step-by-step explanation:
We can calculate the mean as the sum of the product between the number of defective bulbs and its proportion:
[tex]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[/tex]
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:
[tex]s=\sqrt{\sum_i p_i\cdot (X_i-M)^2}\\\\s=\sqrt{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=\sqrt{0.02601+0.00072+0.000363+0.000242}\\\\s=\sqrt{0.027335}\\\\s\approx0.165[/tex]
