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 0.35 probability
$12.50 with 0.40 probability
$15.00 with 0.25 probability
option 3
520
To calculate the lab's budget for next year's rat orders, we first need to find the expected price per 100 rats.
Expected price = (Price1 * Probability1) + (Price2 * Probability2) + (Price3 * Probability3)
Expected price = ($10.00 * 0.35) + ($12.50 * 0.40) + ($15.00 * 0.25)
Expected price = $3.50 + $5.00 + $3.75
Expected price = $12.25
Now, we can calculate the total budget for next year's rat orders.
Total budget = Expected price * Number of weeks * Number of rats per order
Total budget = $12.25 * 52 * 100
Total budget = $63,800
Therefore, the lab should budget $63,800 for next year's rat orders.
To calculate the budget for next year's rat orders, we need to find the expected cost per week for 100 rats. The expected cost is the sum of the product of each price and its corresponding probability.
Step 1: Calculate the expected cost for each price
Expected cost for $10.00 = $10.00 * 0.35 = $3.50
Expected cost for $12.50 = $12.50 * 0.40 = $5.00
Expected cost for $15.00 = $15.00 * 0.25 = $3.75
Step 2: Calculate the total expected cost
Total expected cost = (Expected cost for $10.00 + Expected cost for $12.50 + Expected cost for $15.00) * Number of weeks in a year
Total expected cost = ($3.50 + $5.00 + $3.75) * 52 = $12.25 * 52 = $637
Therefore, the lab should budget $637 for next year's rat orders.