A restaurant chain conducts a random survey of sales of desserts to determine which desserts will be on a new menu. Based on the results of the random survey, which two statements are TRUE?
Responses
A MOST LIKELY, Lava Cake will be on the new menu.
B MOST LIKELY, Lemon Squares will be on the menu.
C MOST LIKELY, Lemon Squares will not be on the menu.
D MOST LIKELY, Macaroons will not be on the menu.
E MOST LIKELY, Banana Pudding will not be the menu.
Without knowing the results of the random survey, no statements can be determined to be true. Therefore, none of the statements can be marked as TRUE.
the results of the random survey are
Cheesecake [[4/20]]
Macaroons [[1/5]]
Lava Cake [[1/4]]
Banana Pudding [[2/10]]
Lemon Squares [[3/20]]
Based on the results of the survey, the following two statements are true:
A) MOST LIKELY, Lava Cake will be on the new menu.
B) MOST LIKELY, Lemon Squares will not be on the menu.
The survey shows that Lava Cake had the highest percentage of sales at 25% (1/4), which makes it very likely to be included on the new menu. On the other hand, Lemon Squares had the lowest percentage of sales at 15% (3/20), which makes it unlikely to be included on the new menu.
Eli is exploring career choices. After randomly surveying 40 companies, he determines that the annual median salary for a computer technician is $72,000. Which two statements are valid inferences for this situation?
Responses
A No computer technician earns more than $72,000 annually.
B Most computer technicians earn at least $72,000 annually.
C 50% of computer technicians earn more than $72,000 annually.
D 50% of computer technicians earn exactly $72,000 annually.
E 50% of computer technicians earn less than $72,000 annually.
Based on the given information alone, the two valid inferences for this situation are:
B) Most computer technicians earn at least $72,000 annually.
C) 50% of computer technicians earn more than $72,000 annually.
A) is not a valid inference as it does not take into account the possibility of technicians earning exactly $72,000 annually or slightly less.
D) is not a valid inference either, as the median salary is the midpoint of all salaries, meaning that there may be a range of salaries above and below $72,000 that are also considered to be the median.
E) is also not a valid inference, as the median salary is not an indication of what percentage of technicians earn less than $72,000. It only tells us that exactly 50% earn more and 50% earn less.
You have answered the question incorrectly. Please view the following explanation below.
50% of computer technicians earn more than $72,000 annually.
50% of computer technicians earn less than $72,000 annually.
The median salary is the "middle" value in the sample data; thus, 50% earn more and 50% earn less than $72,000.
I apologize for my mistake. The valid inferences for this situation are:
C) 50% of computer technicians earn more than $72,000 annually.
E) 50% of computer technicians earn less than $72,000 annually.
As the median salary is $72,000, it means that exactly half of the surveyed computer technicians earn more than $72,000 (inference C) and the other half earn less than $72,000 (inference E).