Question

Marcos and Amaya work at a mobile phone company that offers customers an optional care plan. Customers can choose to pay an extra \[\$50\] when they buy a new phone, and if they damage their screen, then the company will cover the cost of the repair. Marcos and Amaya let \[X\] represent their company's net gain on the sale of a given care plan, and they find the expected value of \[X\] is \[E(X)=\$25\]. Marcos says, "If we sell many of these care plans, the average gain for our company will be about \[\$25\] per plan." Amaya says, "For every \[1{,}000\] customers who buy this care plan, we can expect a net gain of about \[\$25{,}000\]." Whose statement is correct based on the expected value?

Answer 1

Both Marcos and Amaya are correct based on the expected value of $25 per care plan: over many sales, the average gain per plan is $25, and the expected total gain for 1,000 plans is $25,000.

Marcos and Amaya work at a mobile phone company that offers customers an optional care plan. Customers can choose to pay an extra $50 when they buy a new phone, and if they damage their screen, then the company will cover the cost of the repair. Marcos and Amaya let X represent their company's net gain on the sale of a given care plan, and they find the expected value of X is E(X)=$25.

Since they have calculated the expected value of X, which is the average gain or net gain per plan, both Marcos and Amaya's statements are correct. The expected value of $25 represents the average gain for the company per care plan sold, and if 1,000 customers buy this care plan, the company can expect a net gain of about $25,000. So both Marcos and Amaya's statements are accurate based on the expected value.