A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Prices for 100 rats follow the provided distribution. How much should the lab budget for next year's rat orders be, assuming this distribution does not change?
Price
$10.00 with .35 Probability
$12.50 with .4 Probability
$15.00 with .25 Probability
Distribution not shown.
To find out how much the lab should budget for next year's rat orders, we need to calculate the expected cost per week and multiply it by the number of weeks in a year. Here's how we can do that:
Step 1: Calculate the expected cost for each price level.
The expected cost for $10.00 per 100 rats = $10.00 * 0.35 = $3.50
The expected cost for $12.50 per 100 rats = $12.50 * 0.40 = $5.00
The expected cost for $15.00 per 100 rats = $15.00 * 0.25 = $3.75
Step 2: Calculate the weighted average cost.
The weighted average cost is the sum of the expected costs for each price level.
Weighted average cost = ($3.50 + $5.00 + $3.75) / 3 = $4.42
Step 3: Calculate the total budget for next year's rat orders.
Since the lab orders 100 rats per week for each of the 52 weeks in a year, the total number of rats ordered in a year is 100 * 52 = 5200 rats.
Total budget = Weighted average cost * Total number of rats
Total budget = $4.42 * 5200 = $22,984
Therefore, the lab should budget $22,984 for next year's rat orders, assuming the distribution does not change.