Probability/Statistics

Question

1. Avery and Bradley 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 probability that a skid of 50 DVD players will contain at least 3 defective units

a) Help Avery use the binomial distribution to answer this question

1. A PIN number for a bank card consists of 4-6 digits, with no restrictions. How many such PIN numbers are possible? (Repetition is allowed and 0 is allowed in first position) [Hint: consider 3 cases]
2. A family of 7 are to take a photograph.

a) How many arrangements are possible if the triplets (Jack, Bob, Don) are side by side

how many arrangements are possible if the parents are not side by side

Answer 1

1) This is a binomial distribution with n = 50 and p = 0.12. Now,

P(X >= 3) = 1 - P(X <= 2) = 1 - binomcdf(50, 0.12, 2) = 0.9487

2) If it contains four digits, then there are (10)(10)(10)(10) = 10^4 = 10000 different combinations.

If it contains five digits, then there are (10)(10)(10)(10)(10) = 10^5 = 100000 different combinations.

If it contains six digits, then there are (10)(10)(10)(10)(10)(10) = 10^6 = 1000000 different combinations.

Therefore, the total number of combinations is 10000 + 100000 + 1000000 = 1110000.