Answer: Kyra must earn at least 100% on the final exam.
Step-by-step explanation: Kyra's scores have been accumulating from Q1 to Q4 and then the mid term exam. Her scores are outlined as follows;
Q1 = 92, Q2 = 85, Q3 = 88, Q4 = 84, mid-term = 89.
Observe carefully that the data set (number of observed data) is 5.
What she needs now is a final average score of at least 90% after her final exam. She can use this to determine what she needs to score in her final exam. In other words, now that she has a average score, all she needs is a total of all her scores up till her final exam. Note that after writing her final exam, the data set would be six and no longer five.
Before writing her final exam, Kyra's average score was calculated as;
Average = (92 + 85 + 88 + 84 + 89)/5
However after she must have written her final exam, her average would be calculated as;
Average = (92 + 85 + 88 + 84 + 89 + x)/6
Where average is given as 90 and x is the final exam score, you now have
90 = (438 +x)/6
90*6 = 438 + x
540 = 438 + x
Subtract 438 from both sides of the equation
102 = x
Therefore from the results shown, Kyra must score up to 102% in her final exam. However, knowing that she cannot obtain a score higher than 100%, we can conclude that she must score nothing less than 100% (a hundred percent) in her final exam.