Binomial distribution

Question

avery and bradly work at a large electronics manufacturer that produces dvd players.The defective rate on the assembly line has gone up to 12% and the manager wants to know the probabality that a skid of 50 dvd plays will contain atleast 3 defective units

A

a) Help avery use the binomial distribution formula to answer this question

b) help Bradley use nrmal approximation to answer this question

Answer 1

a) Probability contains at least 3 = 1 - probability contains less than three = 1 - (probability contains 0 or 1 or 2)

Binomial distribution formula k successes in n tries where p = probability of success C(n,k) p^k (1-p)^(n-k)

Use binomial formula for k=0, 1, 2 and p = 0.12 and sum probabilities. (answer is 0.9487)

b) want to find P(x >= 3) where x is number of defective units.

= 1 - P(x < 3)

for normal approximation to binomial

mean = np = 50 * 0.12 = 6

sd = sqrt(npq) = sqrt (50 * 0.12 * 0.88) = 2.298

z = x - mean / sd = x - 6 / 2.298

P(x < 3) = P(z < 3 - 6 / 2.298) = P( z < -1.31) = 0.0951

1 - P(x < 3) = 1 - 0.0951 = 0.9049