Question

Question 11

(CO 4) Seventy-nine percent of products come off the line ready to ship to distributors. Your quality control department selects 12 products randomly from the line each hour. Looking at the binomial distribution, if fewer than how many are within specifications would require that the production line be shut down (unusual) and repaired?

Fewer than 7

Fewer than 9

Fewer than 6

Fewer than 10

Question 12

(CO 4) Out of each 100 products, 96 are ready for purchase by customers. If you selected 21 products, what would be the expected (mean) number that would be ready for purchase by customers?

20

96

21

26

Answer 1

11) n = 12

   p = 0.79

P(X < 7) = 1 - P(X > 7)

              = 1 - (P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12))

              = 1 - (12C7 * (0.79)^7 * (0.21)^5 + 12C8 * (0.79)^8 * (0.21)^4 + 12C9 * (0.79)^9 * (0.21)^3 + 12C10 * (0.79)^10 * (0.21)^2 + 12C11 * (0.79)^11 * (0.21)^1 + 12C12 * (0.79)^12 * (0.21)^0)

             = 1 - 0.9755 = 0.0245

P(X < 9) = 1 - P(X > 9)

              = 1 - (P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12))

             = 1 - 12C9 * (0.79)^9 * (0.21)^3 + 12C10 * (0.79)^10 * (0.21)^2 + 12C11 * (0.79)^11 * (0.21)^1 + 12C12 * (0.79)^12 * (0.21)^0)

              = 1 - 0.7674 = 0.2326

P(X < 6) = 1 - P(X > 6)

             = 1 - ( 1 - (P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12))

              = 1 - (12C6 * (0.79)^6 * (0.21)^6 + 12C7 * (0.79)^7 * (0.21)^5 + 12C8 * (0.79)^8 * (0.21)^4 + 12C9 * (0.79)^9 * (0.21)^3 + 12C10 * (0.79)^10 * (0.21)^2 + 12C11 * (0.79)^11 * (0.21)^1 + 12C12 * (0.79)^12 * (0.21)^0)

             = 1 - 0.9948 = 0.0052

P(X < 10) = 1 - P(X > 10)

                = 1 - (P(X = 10) + P(X = 11) + P(X = 12))

                = 1 - P(12C10 * (0.79)^10 * (0.21)^2 + 12C11 * (0.79)^11 * (0.21)^1 + 12C12 * (0.79)^12 * (0.21)^0)

               = 1 - 0.5232 = 0.4768

Since the probabilities for fewer than 6 and fewer than 7 are less than 0.05, so for these two require that the production line be shut down and repaired.

12) p = 96/100 = 0.96

      n = 21

mean = n * p = 21 * 0.96 = 20.16 = 20

Option - a is correct.