Question

Test scores are normally distributed w a mean of 500. convert the given score to a z-score, using the given standard deviation. Then find the % of students who score below 650, if standard deviation is 100. Can you please help Im taking a test and can not figure out

Answer 1

A z-score means that all the values in the data set are centered, by subtracting the mean, and scaled, by dividing by the standard deviation. The result is to convert the data set to have a mean of 0 and a standard deviation of 1.

Answer 2

So one question is, what is the standard deviation?

Answer 3

Is it not the 100?

Answer 4

Sorry, I overlooked that.

Answer 5

:)

Answer 6

OK. So the rule of thumb is that 1 sd away from the mean (in both directions) includes about 68% of the values, 2 sd includes about 95% of the values, and so on.

Answer 7

So the question really asks, if the mean is 500 and the sd 100, what is the z-score of 650. And then, what fraction scores less than that.

Answer 8

Now it's your turn.

Answer 9

so would i subtract 650-500/100?

Answer 10

Yes!

Answer 11

so that gives me 1.5

Answer 12

Now look at this

Answer 13

1/2 of the values are above the mean and 1/2 below.
About 84 % are less than the mean plus 1 sd.
How many are less than 1.5 sd above the mean?

Answer 14

There are tables, you can look it up. Or guess. I'd guess that half way through the next interval is about 6%, because the curve turns up just a bit.

Answer 15

With me?

Answer 16

yep

Answer 17

ok one option is 6.68

Answer 18

So, I'd say it's approximately 84 + 6 = 90% are less than 1.5 sd above the mean.

Answer 19

ok I got what your saying I read the first one wrong

Answer 20

Thank you so much for your help on this :)

Answer 21

yw

Answer 22

have a great night!