Question

http://prntscr.com/occ6jp

Answer 1

@Ferredoxin4

Answer 2

Do you know what is variance in statistics?

Answer 3

squared deviation of a random variable from its mean.

Answer 4

Variance is σ² or s²

Answer 5

Yep

Answer 6

So first you need to calculate standard deviation. Do you know how to do that?

Answer 7

no

Answer 8

\[\sqrt{\frac{ Σ|x-μ| }{ n }}\]

That is the formula.

Answer 9

Sorry, |x−μ| is squared

Answer 10

So you first find the mean. Then find the distance of the points of the mean. Add those distances up. Then divide that summation over the number of terms. Finally, take that quotient and square root it.

Answer 11

By the way that formula is for discrete normal distributions. Binomial, Geometric, Poisson, and other distributions have different formulas.

Answer 12

Did you calculate it? The standard deviation is 2.7857, did you get that?

Answer 13

can you go step by step on how you got that please?

Answer 14

@Vocaloid ?

Answer 15

See in my course I was permitted to use a handheld graphing calculator which includes a feature of calculating the standard deviation. But I can briefly show you the process as it is time-consuming, and it is on your honor to complete that task. Not mine:

Answer 16

First you have to find the mean. Do you know how to do that?

Answer 17

13.2

Answer 18

Correct.

Now you have to find |x−μ|
μ=13.2
x=all the terms.
So you will get in total 10 of those answers as there are 10 terms. You have to subtract each term from the mean and find the absolute value.

Answer 19

Then you will square each of those terms and add the numbers after squaring.

Answer 20

That will be your numerator.

Answer 21

can you help me with that pls?

at least list them for me and I solve it?

Answer 22

The terms are already listed in the question..and you already have the mean..
x={10, 16, 12, 15, 9, 16, 10, 17, 12, 15}
μ=13.2
You have to find
|x-μ| for all of them
So that would be like
10-13.2
16-13.2
12-13.2
And so on..

Answer 23

First do that.
You'll be finding x-μ

Answer 24

10-13.2=-3.2
16-13.2=2.8
12-13.2=-1.2
15-3.2=1.8
9-13.2=-4.2
16-13.12=2.8
10-13.2=-3.2
17-13.2=3.8
12-13.2=-1.2
15-13.2=1.8

Answer 25

Great. Now take the absolute value of those differences

Answer 26

how

Answer 27

Do you know what is absolute value?

Answer 28

non-negative value of x without regard to its sign.

Answer 29

Yes, so find the absolute value of those numbers.

Answer 30

can you do the first one as an example

Answer 31

You're just getting definitions without knowing their significance.

All you have to do to find the absolute value of a number is to remove the negative sign and ensure the value is positive.

For example
|-3.2| = 3.2

Answer 32

if you are going to square them, you don't need to take the absolute value

😣

Answer 33

already got it, what do I do after making them positive?

and no we kinda need to speed it up lol because this is timed

Answer 34

How about @sillybilly123 continues from here.

Thank you.

Answer 35

thats fine if you are busy

@sillybilly123 can you help please?

Answer 36

Just square them. Then add all the numbers after being squared. Then divide it by 10, the #of terms.

There's your variance.

Answer 37

No need to find the square root of it again because variance = s^2

Answer 38

👏

Answer 39

square those numbers and divide them by 10

Answer 40

^

Answer 41

7.76

Answer 42

sorry I was just doing the math lol

Answer 43

Yes correct that's the answer.

Answer 44

http://prntscr.com/occqzu

Answer 45

Same process, just square root the final number after you calculate variance.

Answer 46

oh wow lmao okay this is gonna take long,

is there any shorter or faster way in doing this?

Answer 47

ie in the last example, you got variance of 7.76 so standard dev is square root of that

Answer 48

👍

Answer 49

That's why I told you it's very time consuming unless you use a calculator

Answer 50

Other distributions like binomial and geometric take 2 seconds to find their standard deviation.

Answer 51

so the mean is 12.8?

Answer 52

Close

Answer 53

13

Answer 54

yes

Answer 55

26.2

Answer 56

then what?

Answer 57

Is that your variance?

Answer 58

yes

Answer 59

Well your variance is off

Answer 60

Otherwise, in order to find Standard dev from variance just square root your variance.

Answer 61

Im not sure everything seems right here

Answer 62

Maybe you did a computational mistake. Otherwise the variance is 31.111

Answer 63

I got that

http://prntscr.com/occyqp

Answer 64

You have to use a normal Airulative distribution here. You are asked to find:

\[P(x<70)=P(z_{score}=\frac{ 70-60 }{ 10 })\]

Answer 65

cu mulative* distribution

Answer 66

So that means
P(Zscore=1)
Zscore of 1 means 1 standard deviation above the mean. We can use empirical rule.

Do you know the empirical rule?

Answer 67

Im confused lol

Answer 68

well then what are you confused with?

Answer 69

Are you familiar with the notation and the terms that I just used

Answer 70

Do you know how to calculate probability from a normal distribution?

Answer 71

nope

Answer 72

First you need to find the z-score.
The formula is
(random variable - mean)/standard deviation
Your random variable is 70
mean is 60
SDev is 10

So find the z-score there.
Then you can refer to a standard normal probabilities chart if you'd like, but you'll notice that you z-score is 1 here. Z-score means # of standard deviations away from the mean. Here you are 1 standard deviation above from the mean in a normal distribution. Since it's a 'pretty' number you can use the empirical rule.

Answer 73

(70-60)/10

Answer 74

Yes, that's your z score.

Answer 75

then how do we get the probability

Answer 76

So you got your z-score which can be simplified to 1. Then you would normally go to a probability table http://www.z-table.com/ and find the standard normal probability. But there's no need to do that here. Since it follows the empirical rule you can find the proability.

Answer 77

probability*

Answer 78

What is the empirical rule, thats the thing I dont know what it is so how am I supposed to find the probability

Answer 79

I assume that you would have read the supposed lesson prior to attempting the test, correct?
Otherwise here is empirical rule:

Answer 80

okay and how can I use that to find the probability

Answer 81

So 70 is 1 standard deviation above the mean. So it falls on the 34% plus whatever is below the mean, or 50% of the normal distribution. So that's 50%+34%.

Answer 82

Also, I'll let another user continue from here @Hero . It is expected that you are asking questions because you have difficulty, not because you are blindly attempting a question.