Question

Any stats people?
Some statistics students estimated that the amount of change daytime statistics students carry is exponentially distributed with a mean of $0.72. Suppose that we randomly pick 25 daytime statistics students.
Find the standard deviation.

Answer 1

mean and sd of exponential distribution are same

Answer 2

http://www.phy.ornl.gov/csep/mc/node18.html

Answer 3

Then do you know how to find the distribution of X?

Answer 4

ya

Answer 5

Yay! So how do you find it?

Answer 6

do u mean cummulative distribution

Answer 7

Um, it just says: Give the distribution of X. Then an "X ~ __ (_,_)" I have to fill in the blanks I suppose.

Answer 8

ok.. i think u need to draw the distribution of x.. ( u need to draw a graph)

Answer 9

I have a graph for the average of 25 students.

Answer 10

So I checked the answer. It says it's X~Exp (25/18). How did they get 25/18?

Answer 11

Standard deviation of the Sample of 25 Students.... could be slight of from the general standard deviation.

Answer 12

0.72*25=18

Answer 13

\[\large {25 \over 18}={1 \over 0.72} = \frac 1\mu=\lambda\]

Answer 14

and for 25 students its value ~0.99999

Answer 15

And then how do you do this part? Find the probability that an individual had between $0.79 and $0.96.

Answer 16

related to above question

Answer 17

?

Answer 18

Yes, it's related to the above question.

Answer 19

using cumulative distribution function:
http://upload.wikimedia.org/wikipedia/en/math/1/8/c/18c52cfeafb321ec4c60be0e917388d7.png

\[\large F\left(0.96,{25 \over18}\right)-F\left(0.79,{25 \over18}\right)\]

Answer 20

How do I apply this to the problem?

Answer 21

http://en.wikipedia.org/wiki/Exponential_distribution
If you have your Cumulative distribution function F(x) you can subtract \(F(0.79)\) from \(F(0.96)\)

http://www.wolframalpha.com/input/?i=solve+1-e%5E%28-0.96%2F0.72%29-%281-e%5E%28-0.79%2F0.72%29%29
http://duckduckgo.com/?q=%21wa+-e%5E%28-0.96%2F0.72%29-%28-e%5E%28-0.79%2F0.72%29
\[\large=7.02\%\]

Or you can integrate the probability density function from 0.79 to 0.96

Answer 22

Oh...So this is the last one I didn't get.
The attention span of a two-year-old is exponentially distributed with a mean of about 9 minutes. Suppose we randomly survey 60 two-year-olds.
Calculate the probability that an individual attention span is less than 10 minutes.
This is different from the last problem.

Answer 23

using pdf:
\[\large \int\limits_0^{10}\frac19e^{-x/9}dx\]

using cdf:
\[\large 1-e^{-10/9}dx\]

Answer 24

*** using cdf: just
\[\large 1-e^{-10/9}\]

Answer 25

Do you know how to put that into a ti-84 or ti-83? in terms of cdf, not just the equation.

Answer 26

ti-89 has expcdf() function

can't find it on ti-84

http://www.wolframalpha.com/input/?i=+exponential+distribution+1%2F9