Pandra Manufacturing Obtained the Following Measurements on the Quality Characteristic

Pandra Manufacturing obtained the following measurements on the quality characteristic of the product from its operations in the last few months:
$$\begin{array} { | c | c | } \hline \text { Observed Quality Characteristic, } x & \text { Probability } \\\hline 0.46 & 0.05 \\\hline 0.47 & 0.10 \\\hline 0.48 & 0.12 \\\hline 0.49 & 0.15 \\\hline 0.50 & 0.30 \\\hline 0.51 & 0.12 \\\hline 0.52 & 0.10 \\\hline 0.53 & 0.05 \\\hline 0.54 & 0.01 \\\hline\end{array}$$ The company has determined that no customer will accept any unit that deviates more than 0.04 from the target quality characteristic, T, of 0.5. The company estimates that each rejection would cost the company $500.

Required:
1. Calculate (to the nearest dollar) the cost coefficient, k, for the Taguchi Quality Loss Function (QLF) based on the above information.
2. Determine (to two decimal places) the estimated quality loss, L(x), for each of the observed values of the quality characteristic, x, presented in the above table.
3. Based on the data you generate in response to Requirement 2 above, determine the expected loss, EL(x), given the probabilities presented in the above table. Round final answer to three decimal places.
4. Use the formula EL(x) = k (σ² + D²) to verify your answer in (3), where σ²=∑(x-x̄)f(x) ,and D = the deviation of the mean value of the quality characteristic from the target value =(x̄-T). Round the calculation for D to four decimal places, and the calculation of EL(x) to three decimal places.