Question

Scores on an exam are normally distributed with a mean of 76 and a standard deviation of 10. In a group of 230 tests, how many students score above 96?

Answer 1

First you need to figure out how many "standard deviations" the number you care about (96) is away from your mean. Then, you need to use a normal distribution graph and figure out what percent of people are that many S.D.s above the average. Then you take that percentage and apply it to 230.

Let me know if any of that seems confusing.

Answer 2

Sorry, I stepped away for a second

Answer 3

I have no idea what standard deviations are, or a normal distribution graph :/

Answer 4

Err...is this for a class you're in? Or for SAT/ACT test prep?

Give me a sec.

Answer 5

SAT prep

Answer 6

Explanation of that graph is coming...

Answer 7

Awesome thank you

Answer 8

Let's say a bunch of people take a test. Now, you'd expect most people to do okay on it, and you'd expect a few people to do really really good, and a few people to do really really bad. This is what is known as a normal distribution: the majority of data points fall in the center of the graph, and then taper off as you go toward the ends.

(Stop me if I'm not making sense)

Answer 9

That makes sense so far

Answer 10

So let's take a look at the actual graph. Notice there's this value that looks like a weird "u" called "mu". That's the average of all the data. Notice that 50% did average or better (34.1 + 13.6 + 2.1 + 0.1) and 50% did worse than average.

Now, standard deviation is a measure of how close or far apart data points are. For example, if everyone either got a 76 or a 77 on the test, the standard deviation would be a really small number because everyone did about the same. But if everyone got a 10 or a 99 on the test, the standard deviation would be large because the numbers are so far apart.

Let's say the average test score is 80 and the standard deviation is 5. If you look at that normal distribution graph, each vertical line is a standard deviation away from the average. So 50% of people got an 80 or better. If we move one vertical line over, that value is at 80 + 5 = 85. Well, only 15.8% (13.6 + 2.1 + 0.1) of people did better than an 85. Let's move one more vertical line over...that value is one more S.D. which is 90. Only 2.2% of people did better than a 90%. Let's go one more over, which must be 95. Only 0.1% of people did better than a 95. This works in the opposite direction as well.

Answer 11

So, let's take this step by step. Your average is 76 and your S.D. is 10. The number you care about is 96. How many times do you have to step up from 76 to get to 96?

Answer 12

2?

Answer 13

Yes! So you want to look at the normal distribution graph and then, from the center, go two vertical lines over. What percentage of all data is *past* that vertical line (you have to add up all percentages past the line)?

Answer 14

Wait, does the graph you sent me apply to this as well?

Answer 15

Yes. The normal distribution graph is THE normal distribution graph. It's the one and only. :)

Answer 16

Oh, awesome.

Answer 17

So I'm adding 34.1 and 13.6?

Answer 18

or do I add 2.1 as well

Answer 19

No, you go to the line, and add all the percentages *past* the line. If you think about it, the percentage of people who did better than a 96% should be very small, right?

Answer 20

Yeah, that's why i was confused. So i don't start at the mu, I start at the 1o thing?

Answer 21

2 lines away, not 1 line away.

Answer 22

oh! i start there. I thought I started from the mu then went 2 lines over, adding as i went. So i start at the 2o, then i'd be adding 2.1 and .1? which makes 2.2%

Answer 23

Right. So 2.2% of people did better than 96. And there were 230 tests, so how many people exactly did better than 96?

Answer 24

By the way, do you have choices?

Answer 25

yes, 31, 2, 6, and 14

Answer 26

2.2% is 5.06.. would the answer be 6?

Answer 27

I would think so.

Answer 28

thank you so much. nobody takes the time to explain things out like you do.

Answer 29

It's because I have no life.

Answer 30

I have a problem where I have to jump 4 steps.. how would that work?

Answer 31

haha well at least you're helping people out

Answer 32

oh wait, this is confusing

Answer 33

For a daily airline flight between two cities, the number of pieces of checked luggage has a mean of 380 and a standard deviation of 20. on what percent of the flights would you expect from 340 to 420 pieces of checked luggage?

Answer 34

how do i deal with the 340 to 420 part

Answer 35

340 is how many S.D's to the left? 420 is how many S.D's to the right? Then add up the percentages in between.

Answer 36

are the ones to the left negative?

Answer 37

Oh wait wait wait wait wait. I've made a mistake.

Answer 38

Alrighty

Answer 39

Oh, wait, no, I'm good. Sorry, had a brain fart there for a second.

You can think of them as negative, but basically, if something is below average, you're moving over to the left, and if something is below average you're moving to the right.

So 340 is 2 S.D.s to the left and 420 is 2 S.Ds to the right. So the numbers in between those two vertical lines are 13.6, 34.1,34.1, and 13.6.

Answer 40

Err, if something is ABOVE average, you're moving to the right.

Answer 41

okay.. so is it 4.4%?

Answer 42

no that's ridiculous

Answer 43

Wait, do i add the numbers in between?

Answer 44

which would equal 95%

Answer 45

which makes sense, because the 340 and 420 are very close to 380

Answer 46

I think I've got it.. thank you!

Answer 47

Cool.