Question
Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of
your methods as well as on the accuracy and completeness of your results and explanations.
At a financial institution, a fraud detection system identifies suspicious transactions and sends them to a
specialist for review. The specialist reviews the transaction, the customer profile, and past history. If there is
sufficient evidence of fraud, the transaction is blocked. Based on past history, the specialist blocks 40
percent of the suspicious transactions. Assume a suspicious transaction is independent of other
suspicious transactions.
(a) Suppose the specialist will review 136 suspicious transactions in one day. What is the expected number
of blocked transactions by the specialist? Show your work.
your methods as well as on the accuracy and completeness of your results and explanations.
At a financial institution, a fraud detection system identifies suspicious transactions and sends them to a
specialist for review. The specialist reviews the transaction, the customer profile, and past history. If there is
sufficient evidence of fraud, the transaction is blocked. Based on past history, the specialist blocks 40
percent of the suspicious transactions. Assume a suspicious transaction is independent of other
suspicious transactions.
(a) Suppose the specialist will review 136 suspicious transactions in one day. What is the expected number
of blocked transactions by the specialist? Show your work.
Ask by Ryan Clarke. in the United States
Mar 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expected number of blocked transactions is 54.4.
Solution
Given that the specialist blocks 40% of the suspicious transactions, we can calculate the expected number of blocked transactions by multiplying the total number of suspicious transactions by the percentage of transactions that are blocked.
Let’s denote:
-
as the total number of suspicious transactions. -
as the number of blocked transactions.
We are given that the specialist will review 136 suspicious transactions in one day. Therefore,
The percentage of transactions that are blocked is 40%, which can be represented as 0.4 in decimal form.
The expected number of blocked transactions can be calculated using the formula:
Substitute the given values:
Now, we can calculate the expected number of blocked transactions by the specialist.
Calculate the value by following steps:
Calculate the value by following steps:
- step0: Calculate:
- step1: Multiply the numbers:
The expected number of blocked transactions by the specialist is 54.4 transactions.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution The Deep Dive
To find the expected number of blocked transactions, we can use the formula for expected value in probability. The expected number of blocked transactions can be calculated as:
where:
-
is the total number of transactions reviewed, -
is the probability of a transaction being blocked.
In this case, we have:
-
(the number of suspicious transactions) -
(the probability of blocking a transaction)
Substituting these values into the formula gives us:
Calculating that:
So, the expected number of blocked transactions is approximately 54.4. Since we can’t block a fraction of a transaction, we can say that on average, the specialist would block about 54 transactions.
Now, let’s summarize our work:
- Identified the total number of transactions (
). - Used the blocking probability (
). - Applied the expected value formula.
- Calculated to find the expected number of blocked transactions.
Therefore, we expect roughly 54 transactions to be blocked based on the specialist’s review.
