AVERAGE between 90 and 100%
means not including 90 and 100% but not including 90 or 100%
average=(sum of values in set)/(how many values in the set)
so
4 exams, so there are 4 values
average=(sum)/4
the sum is the known+unknwon
sum=76+99+86+x
so
90<average and average <100
or
90<average<100
lets say average=a
a=sum/number
a=(76+99+86+x)/4
90<(76+99+86+x)/4<100
90<(76+99+86+x)/4 and (76+99+86+x)/4<100
solve each for x and find intersection
90<(76+99+86+x)/4
times 4 both sides
360<261+x
minus 261 both sides
99<x
(76+99+86+x)/4<100
times 4 both sides
261+x<400
minus 261 both sides
x<139
so
99<x<139
since max score is 100
99<x<100
interval notaion is
[99,100]
answer is 2nd one
