A student has a mean score of 88 on five tests taken. What score must she obtain on her next test to have a mean (average) score of 80 on all six tests?
Mean score of tests :
( x1 + x2 + x3 + x4 + x5 ) / 5 = 88 Multiply both sides by 5
x1 + x2 + x3 + x4 + x5 = 88 * 5
x1 + x2 + x3 + x4 + x5 = 440
Mean score of six tests :
( x1 + x2 + x3 + 4 + x5 + x6 ) / 6 = 80
[ ( x1 + x2 + x3 + 4 + x5 ) + x6 ] / 6 = 80
( 440 + x6 ) / 6 = 80 Multiply both sides by 6
440 + x6 = 80 * 6
440 + x6 =480
x6 = 480 - 440
x6 = 60
( x1 + x2 + x3 + x4 + x5 + x6 ) / 6 = 80
x6 = 480 - 440
x6 = 40
To find the score the student must obtain on her next test to have an average of 80 on all six tests, we can use the formula for finding the mean:
Mean = (Sum of all scores) / (Number of tests)
Given that the student has taken five tests and has a mean score of 88, we can find the sum of all five scores by multiplying the mean score by the number of tests:
Sum of all five scores = Mean * Number of tests
Sum of all five scores = 88 * 5 = 440
Now, we need to calculate the sum of all six scores. Since the desired mean score is 80, we can use the formula to find the desired sum of all six scores:
Desired sum of all six scores = Desired mean * Number of tests
Desired sum of all six scores = 80 * 6 = 480
To find the score the student must obtain on her next test, we need to subtract the sum of all five scores from the desired sum of all six scores:
Score on the next test = Desired sum of all six scores - Sum of all five scores
Score on the next test = 480 - 440 = 40
Therefore, the student must obtain a score of 40 on her next test to have an average score of 80 on all six tests.