Solution to Problem 1

The distributions below are binomial with number of trials n and probability of success p.  Determine which of the distributions can be approximated by the normal distribution.  If it can be approximated by the normal distribution, give the mean and standard deviation of the normal approximation.

1. n = 75, p = 0.8
   
   Since np = (75)(0.8) = 60 and nq = (75)(1-0.8) = 15 are both greater than 5, the binomial distribution can be approximated by the normal distribution.
   
   
   
2. n = 30, p = 0.9
   
   Since np = (30)(0.9) = 27and nq = (30)(1-0.9) = 3 are not both greater than 5, the binomial distribution cannot be approximated by the normal distribution.
   
   
   
3. n = 50, p = 0.06
   
   Since np = (50)(0.6) = 3 and nq = (60)(1-0.06) = 47 are not both greater than 5, the binomial distribution cannot be approximated by the normal distribution.
   

Back to the homework handout