STA 291-013  Spring 2000    Computer assignment 4   Due March 7
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Hand written your name and student id on the first page. 
Also type your name once you are inside R,  #Name.......ID......

Problem 1: Find the probability that X is between 3.085 and 4.226
           where X is a normal distributed random variable with
           mu=2, sigma=4 (that is mean and sd).

Problem 2:  Redo example 13 on page 301 use R. 

            first by trial and error. i.e. try different values for g
            so that you get
                      P( X < g ) = 0.07 

            where X is a normal distributed random variable with 
            mu=30, sigma=4

            secondly, try to make use of a new R function called
            qnorm(). See hint below.

Problem 3: Take a look at the web page that you can click and play.

      http://www.ruf.rice.edu/~lane/stat_sim/binom_demo.html 

also you may find this version works better (need netscape 4.06 or higher):

      http://www.ruf.rice.edu/~lane/stat_sim/normal_approx/index.html

           then answer these questions: when (how large n need to be)
           so that the normal approximations are good (error is small)? 
           (a) for p=0.3, and try different n's   
           (b) for p=0.03, and try different n's
           (c) for p=0.99, and try different n's
           (d) for p=0.5, and try different n's

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End of assignment 4
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To find what value g that satisfy P(X < g) = 0.3 where X is normal with
mu=3, sigma=2    do 
> qnorm(0.3, mean=3, sd=2) 

To find what value g that satisfy P(X > g) = 0.3 where X is normal with
mu=3, sigma=2    do 
> qnorm(0.7, mean=3, sd=2)

because P(X > g)=0.3 means P(X<g)=0.7 for normal X ("=" do not matter)
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