Question

Use the normal distribution of SAT critical reading scores for which the mean is 515 and the standard deviation is 105 assume that the variable is x is normally distrubted. What pecent of the SAT verbal scores are less then 650?

Answer 1

somebody please help

Answer 2

Are you familiar with z-scores? If so, please calculate the z score for 650, given that the mean is 515 and the standard deviation is 105.

Answer 3

Are you allowed to use a calculator in this course?

Answer 4

Specifically, a TI-84 calculator?

Answer 5

MM is leading you well, but you don't need a calculator.
The z-score is calculated with \[z=\frac{x- \mu}{\sigma}\]where mu (the weird looking u thing) is the mean and sigma (the weird looking o thing) is the standard deviation.

Answer 6

Yes, and this is called a "standardized score." But first, @jlanding, please tell me and BTaylor about how your instructor has solved similar problems in the past.

BT: jlanding says (although not in this conversation) that he/she has not previously encountered "z-scores."

Answer 7

@jlanding, BTaylor and I need to find out from you what you've already learned about this type of problem. We could explain the problem from scratch, but would prefer to build upon what you already know and have experienced.

Answer 8

Need to get off the Internet, but if either of you responds, I'll respond tomorrow sometime.

Answer 9

@jlanding I will attempt to explain z-scores to the best of my ability.
A normal distribution graph looks something like this: (excuse my incredibly bad artwork)
The middle of the bell curve is the mean (let's use u). The standard deviation (let's use o) is the distance to the next lines (labeled S.D. in the drawing.)
The z-score is the number of standard deviations a value is away from the mean. So, if I have a z-score of +1.5, it is one and a half standard deviations to the right of the mean. A z-score of -2.25 means that the value is two and a quarter standard deviations to the LEFT of the mean. Note that a positive z-score is to the right of the center, and a negative is to the left. The z-score of the mean, incidentally, is 0, since you don't have to move any standard deviations away from the mean. If you are given the mean and the standard deviation, you can find the z-score by using this formula (x is the value you are given, such as 650 in your problem, mu - looks like u - is the mean, sigma - looks like o - is the standard deviation): \[z=\frac{x-\mu}{\sigma}\]
As mathmale mentioned, a graphing calculator can help you figure out the exact proportion above or below the z-score, but the z-score is the first step to finding that proportion. More likely, you will be given a table of z-scores. You find the z-score and, in the table, you will find the proportion below.

I hope this makes sense.