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Answer :
Let's carefully examine each of the statements and determine whether they are true or false based on the given data:
1. Statement a: It is reasonable to estimate that 13 customers out of the first 100 customers next weekend will order baked chicken.
- In the survey of 50 customers, 13 ordered baked chicken. This means that 13/50 or 26% of the customers ordered baked chicken.
- If we apply this percentage to 100 customers, we would expect about 26 customers to order baked chicken, not 13.
- Therefore, this statement is False.
2. Statement b: About 20% of the customers ordered eggplant parmesan this weekend.
- In the survey, 10 customers ordered eggplant parmesan. This is 10/50 = 0.2 or 20% of the total customers.
- So, this statement is True.
3. Statement c: If the restaurant has reservations for 300 people for the next weekend, the chef should prepare about 15 grilled fish entrees.
- In the survey, 5 customers ordered grilled fish, which is 5/50 = 0.1 or 10% of the customers.
- If we apply this percentage to 300 customers, we would expect 0.1 300 = 30 customers to order grilled fish, not 15.
- Therefore, this statement is False.
4. Statement d: About 66% of the customers did not order pasta with vegetables this weekend.
- In the survey, 17 customers ordered pasta with vegetables, which means 50 - 17 = 33 customers did not order it.
- The percentage of customers who did not order pasta with vegetables is 33/50 = 0.66 or 66%.
- Therefore, this statement is True.
5. Statement e: It is reasonable to estimate that 20 out of 200 customers will order roasted turkey as an entrée.
- In the survey, 5 customers ordered roasted turkey, which is 5/50 = 0.1 or 10% of the customers.
- If we apply this percentage to 200 customers, we would expect 0.1 200 = 20 customers to order roasted turkey.
- Therefore, this statement is True.
In summary:
- Statement a: False
- Statement b: True
- Statement c: False
- Statement d: True
- Statement e: True
1. Statement a: It is reasonable to estimate that 13 customers out of the first 100 customers next weekend will order baked chicken.
- In the survey of 50 customers, 13 ordered baked chicken. This means that 13/50 or 26% of the customers ordered baked chicken.
- If we apply this percentage to 100 customers, we would expect about 26 customers to order baked chicken, not 13.
- Therefore, this statement is False.
2. Statement b: About 20% of the customers ordered eggplant parmesan this weekend.
- In the survey, 10 customers ordered eggplant parmesan. This is 10/50 = 0.2 or 20% of the total customers.
- So, this statement is True.
3. Statement c: If the restaurant has reservations for 300 people for the next weekend, the chef should prepare about 15 grilled fish entrees.
- In the survey, 5 customers ordered grilled fish, which is 5/50 = 0.1 or 10% of the customers.
- If we apply this percentage to 300 customers, we would expect 0.1 300 = 30 customers to order grilled fish, not 15.
- Therefore, this statement is False.
4. Statement d: About 66% of the customers did not order pasta with vegetables this weekend.
- In the survey, 17 customers ordered pasta with vegetables, which means 50 - 17 = 33 customers did not order it.
- The percentage of customers who did not order pasta with vegetables is 33/50 = 0.66 or 66%.
- Therefore, this statement is True.
5. Statement e: It is reasonable to estimate that 20 out of 200 customers will order roasted turkey as an entrée.
- In the survey, 5 customers ordered roasted turkey, which is 5/50 = 0.1 or 10% of the customers.
- If we apply this percentage to 200 customers, we would expect 0.1 200 = 20 customers to order roasted turkey.
- Therefore, this statement is True.
In summary:
- Statement a: False
- Statement b: True
- Statement c: False
- Statement d: True
- Statement e: True
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