Answer:
(d) 19
Explanation:
The average of a set of numbers is their sum, divided by the number of numbers in the set.
Setup
Let s represent the score Danielle must get on her sixth test. Then her average will be ...
average = (17 +19 +20 +14 +16 +s)/6
Danielle wants that to be 17.5, so we have ...
17.5 = (86 +s)/6
Solution
Multiplying by 6, we get ...
105 = 86 +s
19 = s . . . . . . . . subtract 86
Danielle must score 19 on her 6th test to have a mean of 17.5.
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Additional comment
We can also figure this by considering the deviations from the average Danielle wants. They must total zero. The sum of deviations of the given scores is ...
(17 -17.5) +(19 -17.5) +(20 -17.5) +(14 -17.5) +(16 -17.5)
= -0.5 +1.5 +2.5 -3.5 -1.5 = -1.5
To bring the total to zero, Danielle must score 17.5 +1.5 = 19.