Answer to Question #152050 in Statistics and Probability for JG

Question

A company produces mobile phones of which 3% are defective.
a) If 20 mobile phones are selected for testing, what is the probability that exactly 8 are defective?
b) If 12 mobile phones are selected for testing, what is the probability that more than 2 are not defective?
c) If a distributor gets a shipment of 1000 mobile phones, how many of these mobile phones do we expect to be defective, and what is the standard deviation?

Answer 1

$(a)P(x=8)=C_{8}^{20}(0.03)^{8}(0.97)^{20-8}\\ \approx 5.735 \times 10^{-8}\\ (b)P(x> 2)=1-P(x\leq2)\\ =1-[P(x=0)+P(x=1)+P(x=2)]\\ =1-[C_{0}^{12}(0.97)^{0}(0.03)^{12-0}\\+C_{1}^{12}(0.97)^{1}(0.03)^{12-1}]+C_{2}^{12}(0.97)^{2}(0.03)^{12-2}]\\ \approx 1\\ (c) E(x)=1000(0.03)=30,\\ \sigma_{x}=\sqrt{1000(0.03)(0.97)}\approx 5.394$