CK-12 Probability and Statistics - Advanced

http://www.ck12.org Chapter 4. Discrete Probability Distribution

2. Thebinomial probability distributionis:

p(x) =

(

n

x

)

px( 1 −p)n−x=

(

n

x

)

pxqn−x

3. For the binomial random variable:

Themeanisμ=n p

Thevarianceisσ^2 =n pq=n p( 1 −p)

Thestandard deviationisσ=

√

n pq=

√

n p( 1 −p)

Review Questions

1. Supposexis a binomial random variable withn= 4 ,p= 0 .2. Calculatep(x)for the values:x= 0 , 1 , 2 , 3 , 4 ,5.
   Give the probability distribution in tabular form.


2. Supposexis a binomial random variable withn=5 andp= 0 .5.
   a. Displayp(x)in tabular form.
   b. Compute the mean and the variance ofx.


3. Over the years, a medical researcher has found that one out of every ten diabetic patients receiving insulin
   develops antibodies against the hormone, thus requiring a more costly form of medication.
   a. Find the probability that in the next five patients the researcher treats, none will develop antibodies
   against insulin.
   b. Find the probability that at least one will develop antibodies.

Review Answers

1.

x 0 1 2 3 4

p(x) 0. 4096 0. 4096 0. 1536 0. 0256 0. 0016

1.

x 0 1 2 3 4 5

p(x) 0. 031 0. 157 0. 312 0. 157 0. 031

2. 
   
   
   
   2. 5 , 1. 25
   
   
   
   

1. 0.590;

2. 0. 410