Need an answer for STATISTICS problem before 3 o'clock?

Question

The SAT scores of 1.4 million students are roughly normal with a mean of 1026 and standard deviation of 209.

I found the proportion of all students who took the SAT that had scores of at least 700 in the first problem and the answer came out to be 94%.

The next question is what is the 60% percentile of the SAT score?

I need to be able to show work without using a calculator..answers are much appreciated!!!

How is everybody getting that the z-score is approximately .25? that's all i need to know to understand the concept, then i've got it. thanks everyone.

Answer 1

I don't know if that can help and you can reverse the process

Answer 2

I am not sure whether I am correct because,
(1) The 1.4 million is too large a sample and can be considered as the total population.
Hence the mean 1026 and SD 209 are population mean and standard deviation.
To find the 60th percentile, we want the score such that 60 % of students scored below it.
i.e. the area under the normal curve is 0.60.
The z score that corresponds to this 60 % is approximately 0.25.
P[(x-1026)/209) < 0.25]=0.60
(x-1026)/209 =0.25
solving x=1078.25=1078 (approximately)
So, to find the 60th percentile, the information you have is not needed at all even if you thought 1.4 million were your sample size.
1. I did not use 1.4 million as sample size
2. I used 209 as SD rather than 209/sqrt(1.4 million)
3. I did not use the 94 % you found and try to incorporate it in finding the 60th percentile.
4. There is only one question (the next question?), namely "What is the 60th percentile?"

Answer 3

This is very much like the problem you just completed only this time it is X that is missing.

The 60th percentile is the point (score) that 60% of all the scores fall below. 60% of scores will be below it, 40% of score will be above it.

For problems like this, I like to draw a picture of a normal curve and then sketch in the area or number I'm looking for.

Since your data set is normal (as you stated) the mean will be the same as the median. So already you know that 50% of all scores are going to fall below 1026. So now find the score that 60% of all other scores fall below.

First you need to find a z-value that is going to match up with that spot. Look at the chart in your book for the area under the curve.

The z-value at the median is 0 and you know you need a z that is higher than the median so it has to be positive.

The z you are looking for is going to be approximately 0.25.

Once you find what exactly that value is, plug all the info you have into the formula you typically use for finding a z-score and you'll have your answer.

z= (x - the mean) / standard deviation

if z = .25, your equation will look like this

.25 = (x - 1026) / 209

so 209(.25) = x- 1026 and thus x = 209(.25) + 1026

Draw a picture of the normal curve and put in z values and your real values so you can see what is happening.

Good luck.

Answer 4

First, you need to determine the z-score value from a standard normal table where the percentage of values below that is 60%. From my look, I see z = 0.2533.
A z-score of 0 would be the 50th percentile and the mean of a standard normal, so the z = 0.2533 makes sense to me.

Now solve the equation.

(X - 1026) / 209 = 0.2533

X = 1078.

60% of SAT scores are at or below 1078.

Answer 5

You need a table of Z-scores, my good lady.

0.6 is 0.1 above the mean. According to the table, that's a Z-score of roughly 0.255 (standard deviations above the mean, that is).

1026 + 0.255 * 209 = 1079.295

Print out the Z-score table and staple it to your work.

Answer 6

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