Question

Kevin works for a company that manufactures solar panels. In a large batch of solar panels, about 1 in 200 is defective. Suppose that Kevin selects a random sample of six solar panels from this batch. What is the probability that none of the solar panels are defective?

Answer 1

Answer:

probability that none of the solar panels are defective = 0.97

Step-by-step explanation:

Proportion of solar panels that are defective, p = 1/200 = 0.005

Proportion of solar panels that are not defective, q = 1 - p = 1 - 0.005

q = 0.995

Sample size, n = 6

probability that none of the solar panels are defective, P(X=0)

Note: $P(X=r) = nCr p^{r} q^{n-r}$

$P(X=0) = 6C0 * 0.005^{0} * 0.995^{6-0}\\P(X=0) = 6C0 * 0.005^{0} * 0.995^{6}\\P(X=0) = 1 * 1 * 0.9704\\P(X=0) = 0.97$