h3 - Normal Dist

# h3 - Normal Dist - Page 1 of 4 Stat 201 Handout - updated...

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Stat 201 Handout -- updated version (June 4, 2003) More on Coin Tossing and the Normal distribution Review: Examples from class 1. Toss coin 5 times. Random variable of interest is X=# heads . { Computed and graphically displayed probability distribution for X . { Demonstrated idea of P(X=x) being equal to the area associated with x under the probability distribution histogram . { Introduced idea of discrete r.v.'s and continuous r.v.'s. 2. Randomly guess answers on exam. R.v. of interest is X=exam mark out of 100 . Know X has normal distribution with mean 21.7 and SD 8.49. { Discussed P(X=50)=0 . (Similarly for P(X=x) for any single value of x .) { Computed P(pass)=P(X >= 50) : ± Need to standardize X (change scale to Z -scale): --------------|---------|------------------|////////////-> x 21.7 30.19 50 --------------|---------|------------------|////////////-> z 0 1 50-21.7 --------- 8.49 P(X>=50)=P ( (X-21.7)/8.49 >= (50-21.7)/8.49 ) = P(Z >=3.33) z Use normal table on pp. 538-539 to find areas under the normal curve: { areas listed are left tails -- correspond to P(Z<=z) for given values of z z Read off P(Z<=3.33)=P(Z<3.33)=0.9996 . So P(X>=50)=P(Z>=3.33)=1-P (Z<3.33)=1-0.9996=0.0004 . Binomial Distribution For Example 1 above, we have a special name for the distribution of X . We say " X has a binomial distribution with n=5 and p=0.5 ." We write X~Bin(n=5,p=0.5) . Definition A binomial distribution results from a random operation involving n independent success - failure trials with a common probability of success p . The total number of successes has a Bin(n,p) Page 1 of 4 3/26/2011 http://www.stat.sfu.ca/~sgchiu/Grace/S201/Handouts/h3.html

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distribution. More examples of binomial r.v.'s a. For any given beef-cow, there is a 0.2 probability for it to have BSE (mad cow disease). Your herd has 38 animals. X is the total number of cows in your herd that have BSE. So X~Bin(n=38,p=0.2) . b. From
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## This note was uploaded on 01/23/2012 for the course STAT 201 taught by Professor Staff during the Fall '03 term at Simon Fraser.

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h3 - Normal Dist - Page 1 of 4 Stat 201 Handout - updated...

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