Question

an electronics store gives customers the option of purchasing a protection plan when customers buy a new television. the customer pays $100 for the plan, and if their television is damaged or stops working, the store will replace it for no additional charge. the store knows that 4% of customers who buy this plan end up needing a replacement that costs the store $1,000 each. here is a table that summarizes the possible outcomes from the stores perspective: |replacement?|cost|net gain (x)| |---|---|---| |yes|$1,000|-$900| |no|$0|$100| let x represent the stores net gain from one of these plans. calculate the expected net gain e(x).

Explanation:

Step1: Identify probabilities and values

The probability of "Yes" (replacement) is \( 4\% = 0.04 \), with net gain \( X = -900 \). The probability of "No" (no replacement) is \( 1 - 0.04 = 0.96 \), with net gain \( X = 100 \).

Step2: Use expected value formula

The formula for expected value \( E(X) \) is \( E(X) = \sum (x_i \cdot P(x_i)) \), where \( x_i \) are the values of \( X \) and \( P(x_i) \) are their probabilities.

So, \( E(X) = (-900 \cdot 0.04) + (100 \cdot 0.96) \).

Step3: Calculate each term

First term: \( -900 \cdot 0.04 = -36 \).

Second term: \( 100 \cdot 0.96 = 96 \).

Step4: Sum the terms

\( E(X) = -36 + 96 = 60 \).

Answer:

\( 60 \)