Question

your company has an agreement according to which it can return to the supplier shipments where...

your company has an agreement according to which it can return to the supplier shipments where 3+ containers have faulty materials). According to the same agreement, your company is entitled to compensation on a progressive scale. Specifically, a clause in the agreement states that the supplier will compensate your company as follow: If more than 4 but less than 7 containers are faulty, the supplier will pay a penalty of $10,000; If there are 7 or more faulty containers but less than 10 then the penalty would increase to $15,000, and; if at least 10 are faulty the supplier pays a penalty of $20,000.

(1) What are the chances that the supplier will have to pay a penalty?

(2) What are the chances that the supplier will not have to pay a penalty?

(3) What is the probability that the supplier will have to pay at most $15,000?

(4) What is the likelihood that the supplier will have to pay $15,000 or more?

Hint 1: When working with complex events it is important to pay close attention to the following keywords: lass than, more than, X or more, X or less, no more than, no less than, at most, and at least.

Hint 2: Create a new random variable, PenaltyPaidBySupplier. List the possible outcomes and specify their probabilities

Number of faulty containers Frequency
0 93
1 7
2 5
3 4
4 2
5 1
6 1
7 1
8 2
9 1
10 or more

3

Homework Answers

Answer #1

1.

P(penalty) = sum of freq ((no. of faulty conatiner) > 4) / total freq.

= 9/120 = 3/40 = 0.075

P(penalty) = 0.075

2.

P(no penalty) = sum of freq ((no. of faulty conatiner) <= 4) / total freq.

= 111/120 = 0.925

3.

P(penalty<=15000$) = sum of freq ((no. of faulty conatiner) <10) / total freq.

= 117/120 = 39/40 = 0.975

4.

P(penalty >= 15000$) = sum of freq ((no. of faulty conatiner) >= 7) / total freq.

= 7/120 = 0.05833

P.S. (please upvote if you find the answer satisfactory)

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