Table 13-6
Paul prepares a variety of Creole and Cajun dishes to the delight of his diners at his restaurant in the French Quarter.Demand for crawfish etouffee follows this historical distribution:
Each recipe of crawfish etouffee calls for two sticks of butter which the prep chef must buy down the block at a local grocery store.Paul would like to put in a special butter refrigerator and needs to estimate the capacity he would need if he orders twice a week from his butter supplier.He decides to simulate two weeks of this process using the historical distribution mapped to random numbers ranging from 01-00 and the random number table below.

-At what level of nightly order for etouffee does the cumulative probability reach 50% for the scenario shown in Table 13-6?
A)22 orders
B)24 orders
C)26 orders
D)28 orders

Question

Table 13-6
Paul prepares a variety of Creole and Cajun dishes to the delight of his diners at his restaurant in the French Quarter.Demand for crawfish etouffee follows this historical distribution:
  Each recipe of crawfish etouffee calls for two sticks of butter which the prep chef must buy down the block at a local grocery store.Paul would like to put in a special butter refrigerator and needs to estimate the capacity he would need if he orders twice a week from his butter supplier.He decides to simulate two weeks of this process using the historical distribution mapped to random numbers ranging from 01-00 and the random number table below.
 
-At what level of nightly order for etouffee does the cumulative probability reach 50% for the scenario shown in Table 13-6?
A)22 orders 
B)24 orders 
C)26 orders 
D)28 orders

Quizplus · Accepted Answer

To find the level of nightly order for etouffee that corresponds to a cumulative probability of 50%, we need to use the cumulative frequencies column in the random number table.

First, we need to calculate the total number of orders for the two-week simulation. From the historical distribution, we can see that the total number of orders is:

(5 x 10) + (10 x 15) + (8 x 20) + (7 x 25) + (3 x 30) = 405

Since Paul orders twice a week, he would need to order 405/2 = 202.5 times per week. Since he can't order half an order, let's round up to 203 orders per week.

Now we can use the random number table to find the cumulative probability of reaching 203 or fewer orders. Starting with the first random number, we add the corresponding frequency to a running total until we reach a cumulative frequency that is at least 203.

The cumulative probabilities for each row are:

0.20
0.50
0.77
0.93
1.00

The cumulative frequency for row C is 20 + 15 + 20 + 25 = 80, which is the first row with a cumulative probability greater than 0.50.

However, this only covers one week. To simulate two weeks, we need to double the number of orders. So, the level of nightly order for etouffee that corresponds to a cumulative probability of 50% for the scenario in Table 13-6 is:

80 x 2 = 160 orders per week
160/7 = 22.86 (rounded to the nearest whole number)

Therefore, the answer is choice C: 26 orders.

Table 13-6 Paul Prepares a Variety of Creole and Cajun Dishes to Dishes