Question

Professor Mean takes a 4-sided die to the grocery store, starts at one end of the chips aisle, and travels to the other end. At each different kind of chips, Dr. Mean rolls the die. If it comes up a 4, he purchases the chips for the party. There are 40 different kinds of chips in the aisle. Define random variable x = number of types of chips purchased out of 40. What is the mean of the random variable x? What is the standard deviation of the random variable x?

Answer 1

hello

Answer 2

hello

Answer 3

What have you got so far? Or were you just saying hi to the stats crowd? :D

Answer 4

i think i know what to do

Answer 5

the "there are 40 different kins of chips" thing is what makes me think im doing it wrong

Answer 6

i was reading it what did it say?

Answer 7

It was just the formula for expected value, but I deleted it because I misstyped it. I will be back in a few minutes, sorrry.

Answer 8

Professor Mean? woah

Answer 9

Devation is 6 because there are only 6 different numerical otcomes

Answer 10

@xartaan I got this

Answer 11

sry i was afk xD

Answer 12

yes

Answer 13

did i lose connection?

Answer 14

It's 4-sided.
Is each side equally likely to occur?

Answer 15

yea

Answer 16

So, what is the chance that a 4 will show if you tossed the die once, if each side is equally likely?

Answer 17

1/4

Answer 18

So, now 1 out of every 4 tosses will be (on average) a 4.

You agree?

Answer 19

yes

Answer 20

Ok, if I tossed the die 4 times how many times would 4 show up (on average)?

Answer 21

once

Answer 22

Correct!

If I tossed the die 8 times, how many times would 4 show up (on average)?

Answer 23

twice

Answer 24

That's right!

So for every 4 tosses, I get 1 4 (on average).

So if I toss it 40 times, how many times does 4 show up (on average)?

Answer 25

6 times

Answer 26

When we tossed it 4 times

We get a 4 (on average) \(4 \times\cfrac{1}{4}=1\) fours
_______________________________________________________

When we tossed it 8 times

We get a 4 (on average) \(8 \times\cfrac{1}{4}=2\) fours
_______________________________________________________

Do you see the pattern?

Answer 27

If we tossed it 40 times,

We get a 4 (on average) \(40\times\cfrac{1}{4}=?\) fours

Answer 28

hmm i see its 8

Answer 29

so hen what is the mean of variable x then is it the same thing

Answer 30

40 x 1/2?

Answer 31

(making sure you are checking)

The mean number value of x is the average number of times that 4 shows up when you through the die 40 times.
$$
40\times\cfrac{1}{4}
$$

Answer 32

*throw

Answer 33

okay i got hat i was just confused with the 1/2

Answer 34

so is the standard dev is 6 like that other person said?

Answer 35

Not quite,, recall the definition of the Var is E[X^2] - [E(X)^2] .. You know the mean is 10 so that's the easy half... Sorry trying to do this from my phone, hope that's clear this far though

Answer 36

I assume that you understand now how to get the average N * p, where p = 1/4.

Next, the standard deviation is computed similarly

$$

\large{
\sigma^2=Npq
}
$$
Where q=1-p
So the standard deviation is
$$
\sigma=\sqrt{40\times\cfrac{1}{4}\times\cfrac{3}{4}}\approx2.74
$$
These formulas assume that this whole process can be modeled by the binomial distribution - http://en.wikipedia.org/wiki/Binomial_distribution.

It is binomial because the die either IS or IS NOT a 4 - and so you can think of this as either being a 1 or a 0 -- binary and hence the binomial distribution.

I hope this made sense.