Stat 2000, Section 001, Homework Assignment 12 (Due 4/21/2000 in class)

• 0) Reading: Section 5.1, 5.2
  
  
• 1) Please work on the following textbook questions in Moore/McCabe:
  
  
  • a) Exercise 5.1, 5.2, 5.4, 5.6, 5.11, 5.12 (1 Point each)
    
    
  • b) Exercise 5.18, 5.20, 5.21 (2 Points each)
    
    
  • c) Exercise 5.24, 5.26, 5.30, 5.34 (1 Point each)
    
    
• 2) Recall the bahavior of the manipulated coin (70% chance of head) we discussed in our 4/10/00 lecture. Suppose we toss this coin 1000 times. (3 Points)
  
  
  • a) What are mean, variance, and standard deviation for a random variable X that is related to this coin?
    
    
  • b) What is the probability to end up with 700 to 900 times head with this coin? Use an appropriate approximation to calculate this probability.
    
    
  • c) And what is the probability to end up with 700 to 900 times head with a "fair" coin? Use an appropriate approximation again to calculate this probability.
    
    
• 3) Work with the Central Limit Theorem applet at
  http://www.stat.sc.edu/~west/javahtml/CLT.html
  
  Roll 3 dice once, 10 times, 50 times, 100 times, 500 times and decribe your observations. How does this compare to rolling 1 die the same number of times? And what happens if you roll 5 dice the same number of times? (3 Points)
  
  
• 4) Work with the Normal Approximation to Binomial applet at
  http://www.ruf.rice.edu/~lane/stat_sim/normal_approx/index.html
  
  Select N = 5 and set "from" = 2 and "to" = 4. Then use p = 0.1, 0.5, and 0.8, and report what the exact binomial probabilities and the probabilities by the normal approximation are.
  
  Similarly, work with N = 50, "from" = 20 and "to" = 30. Use p = 0.4, 0.5, and 0.7 here. Report the probabilities.
  
  Finally, look at N = 500, "from" = 240, "to" = 260, and p = 0.5 and report the probabilities.
  
  Experiment with some other parameters and summarize your findings in two or three sentences. (3 Points)