Final answer:
The expected value of X is calculated using the sum of all possible values of X times their respective probabilities. For the repair facility's pricing strategy, they compare the expected earnings from a flat fee of $65 with the expected value of the variable charge formula E(150/(5-X)) to determine which option is more beneficial.
Step-by-step explanation:
To calculate the expected value of a random variable X, you sum the products of each possible value of X times the probability of that value occurring. From the data provided, it looks like the student needs assistance with calculating the expected value E(X) given a probability distribution, as well as the expected value of a transformation of this variable, E(5−X).
Next, the question is related to determining a pricing strategy for a repair facility. The facility needs to choose between a flat fee of $65 or a variable cost that depends on the random variable X. The expected earnings from the variable charge would need to be calculated to compare both pricing strategies.
For the expression E(150/(5−X)), we must remember that the expected value of a reciprocal or a transformation is not directly the reciprocal of the expected value of the original variable. Instead, we would have to calculate this expected value based directly on the provided probability distribution of X and the specific transformation in question. The repair facility would then compare the expected earnings from this variable charge with the flat fee of $65 to determine which pricing option is better.