Find the raw scores that cut-off the most extreme 5% under the normal distribution's curve that has a mean of 12 and standard deviation of 3.5.

5.14 and 18.86

Step-by-step explanation:

They give us the following information:

mean (m) = 12

standard deviation (sd) = 3.5

For cutting extreme 5% under the normal distribution curve standard normal score is + - 1.96

we have to:

z = (x - m) / sd

Lower limit is

-1.96 = (x -12) /3.5

-6.86 = x - 12

x = 5.14

Upper limit is

1.96 = (x -12) /3.5

6.86 = x - 12

x = 18.86

Therefore, the raw scores are 5.14 and 18.86