\"Scores on an English test are normally distributed with a = 70 and a s.d. = 12. Find the score that seperates the top 20% from the bottom 80%\". I am confused on what ~the score~ would be, I assume a z-score but this question has stumped me and I would apreciate your help. Solution = 70 = 12 The probability that the z score is greater than b is 20%: P(z > b) = .20 So first, we need to find the value of b that makes that probability true. Looking at a standard normal table, we find that z=.84 has approximately 20% to the right. P(z > .84) = .20 Recall taht z = (x-)/, when x is a single observation So now we have z = .84 = (x-)/, where x is our unknown, =70, and =12 .84 = (x-70)/12, solve for x .84*12 + 70 = x = 80.08 A score of 80.08 seperates the top 20% from the bottom 80%..

1. "Scores on an English test are normally distributed with a = 70 and a s.d. = 12. Find the score
that seperates the top 20% from the bottom 80%".
I am confused on what ~the score~ would be, I assume a z-score but this question has stumped
me and I would apreciate your help.
Solution
= 70
= 12
The probability that the z score is greater than b is 20%: P(z > b) = .20
So first, we need to find the value of b that makes that probability true.
Looking at a standard normal table, we find that z=.84 has approximately 20% to the right.
P(z > .84) = .20
Recall taht z = (x-)/, when x is a single observation
So now we have z = .84 = (x-)/, where x is our unknown, =70, and =12
.84 = (x-70)/12, solve for x
.84*12 + 70 = x = 80.08
A score of 80.08 seperates the top 20% from the bottom 80%.