To solve the problem of determining how much the lab should expect to spend on shipments each week based on the given probability distribution, we need to calculate the expected value of the weekly cost. The expected value is a measure of the center of a probability distribution and is computed by multiplying each possible value by its corresponding probability and then summing all of these products.
Here are the steps to find the expected weekly cost:
1. Identify the possible prices and their corresponding probabilities:
- Price of [tex]$8.00 with a probability of 0.15.
- Price of $[/tex]12.00 with a probability of 0.45.
- Price of [tex]$16.00 with a probability of 0.40.
2. Multiply each price by its corresponding probability:
- $[/tex]8.00 * 0.15 = [tex]$1.20
- $[/tex]12.00 * 0.45 = [tex]$5.40
- $[/tex]16.00 * 0.40 = [tex]$6.40
3. Sum these products to find the expected value:
- $[/tex]1.20 + [tex]$5.40 + $[/tex]6.40 = [tex]$13.00
Therefore, the lab should expect the shipments to cost \$[/tex]13.00 per week on average.
