Question

math help
A normal random variable X has mean 40 and standard deviation 16. Find the area under the normal curve above the interval 16-60.

0.7324

0.8962

0.8276

0.8089

Answer 1

How many standard deviations is 16 and 60 from the mean?

Answer 2

no idea

Answer 3

You have to find the z-score

Do you know how to find z-score?

Answer 4

no I dont :(

Answer 5

\(z=\large\frac{x-\mu}{\sigma}\)

\(\mu\)=mean
\(\sigma\) = Standard deviation
x = your value (In this case, its 16 and 60)

Answer 6

oh I see

Answer 7

So I'll do the first one
\(z=\large \frac{16-40}{16}\)

\(z=-1.5\) standard deviations from the mean

Answer 8

so the second is 1.25?

Answer 9

\(z=\large \frac{60-40}{16}\)

\(z=1.25\)

Right

Answer 10

then what do I do?

Answer 11

i am so confused

Answer 12

this isnt helping

Answer 13

He is doing a great job :) I can understand I just don't know what to do next lol

Answer 14

For this you need to use the z-score table

Answer 15

Sorry that response took so long btw

Answer 16

its fine :) and if you dont mind can you please show me how to use it

Answer 17

Okay so the left shows the z-score, the top part is if there are more than 1 numbers after the decimal

Ex. -1.5 is 0.668 but -1.52 is -.643

Answer 18

Correction: -1.52 is 0.643*

Answer 19

oh so we ignore 0.668?

Answer 20

No no, we use 0.668 because we had -1.5 as our z-score before, the -1.52 was just an example on how to use it

Answer 21

This is the positive z-score values

Answer 22

^We're missing 1.25, so do you know how to find it using that table?

Answer 23

is it .8944?

Answer 24

Right, so the issue with this is that is includes all of the values from 0-1.25, in order to get rid of this, we subtract 0.8944-0.0668
(What we got from the z-score of -1.5 and the z-score of 1.25)

Answer 25

right

Answer 26

And that should be your answer

Answer 27

ooooh I seeeeee omg I finally get it!! Thank you sooo much! I appreciate it :)

Answer 28

I felt like I explained this too quickly, if you want me to review another question I could try to re-explain it

Answer 29

That would be great! omg your thank you :)

Answer 30

Yeh

In a nutshell,
______________________________________________________________________
Find the z-score using the equation \(z=\large \frac{x-\mu}{\sigma}\)

Then use the tables I gave you to find the % area (Careful for the positive and negative on both)

Subtract the highest z-score value from the lowest z-score and that should give you your answer
______________________________________________________________________

Answer 31

Ok this is a similar one

A normal distribution has mean 200 and standard deviation 50. Find the area under the normal curve from the mean to 224

Answer 32

Make a new post before this gets laggy :P

Answer 33

oh ok

Answer 34

I just wanted to say thank you so much for this! I came back to review for my finals and this really helped!

Answer 35

Haha no problem