Question

A company that produces fine crystal knows from experience that 15% of its goblets havecosmetic flaws, while the remaining 85% are flawless.(a) (8 points) If eight goblets are selected at random, what is the probability that exactly twohave flaws

Answer 1

The probability that exactly two have flaws is P (x=2) = 0.2376

Explanation:

Here

Success= p= 0.15

Failure = q= 0.85

total number= n= 8

Number chosen = x= 2

Applying the binomial distribution

P (x=x) = nCx p^x(q)^n-x

P (x=2) = 8C2 0.15 ²(0.85)^8

P (x=2) = 0.2376

The success is chosen about which we want to find the probability. Here we want to find the probability that exactly two have flaws so success would be having flaws therefore p = 0.15