a) Show that the normal approximation to the binomial can appropriately be used to calculate probabilities about x. np = ? n(1 – p) = ?     Both np and n(1 – p) ≥ ? b) Make continuity corrections for each of the following, and then use the normal approximation to the binomial to find each probability:

MATLAB: An Introduction with Applications
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Suppose that x has a binomial distribution with n = 201 and p = 0.45.

(a) Show that the normal approximation to the binomial can appropriately be used to calculate probabilities about x.

np = ?

n(1 – p) = ?

 
 
Both np and n(1 – p) ?

b) Make continuity corrections for each of the following, and then use the normal approximation to the binomial to find each probability:

 
 
     
1. P (x = 79)  
2. P (x ≤ 99)  
3. P (x < 72)  
4. P (x ≥ 101)  
5. P (x > 104)           
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