The distribution of student scores on the quantitative...

The distribution of student scores on the quantitative section of the SATs have an approximately normal distribution with a mean score of 501 points, and a standard deviation of 85 points. Suppose a college with competitive admissions will only accept students who scored at least a 550 on the quantitative section of the SATS. What proportion of students will NOT qualify for acceptance at the that college based on SAT scores? Provide all four decimal places in your answer.

Transcript

00:01 Okay, we're dealing with the distribution of student scores on the sat section.

00:05 Told the mean is 501, standard deviation is an 85.

00:09 We're told it's a competitive school that's only going to accept scores 550 or higher.

00:15 So i'm going to call 550 the cut score.

00:18 Because this was told to us to have a normal distribution, the first thing we want to do is calculate a z score.

00:24 It's very important that that was a normal distribution.

00:28 Okay, so z is going to equal.

00:34 The x value, which is your cut score, 550, minus the mean of 501 over the standard deviation of 85.

00:53 Okay, if you divide that out, you're going to end up getting 0 .57677 .7.

01:08 I'm going to stop there.

01:10 Okay, because that's actually good enough if you were asked to solve this question.

01:14 Using a z table more than likely you have a calculator available but we're going to take a look at this z table first so what the z table is going to show you is we have our normal distribution and that would be in the shape of what we call bell curve and the center here is our median five hundred and one and we're looking at this cut score of 550 which really isn't that much higher.

01:52 Okay, and we want to find the probability or the proportion that is lower than that value.

02:00 So we're looking in this area here.

02:05 When you found a z score for this of 0 .577647, you're doing what's called standardizing the score.

02:17 And now we can use our z table chart to figure out the answer.

02:22 Okay, so all i do is go in the z column and find in this case 0 .5...

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