CK-12-Basic Probability and Statistics Concepts - A Full Course

http://www.ck12.org Chapter 4. Probability Distributions

P(X=a) =nCa×pa×q(n−a)

P(3 heads) = 5 C 3 ×p^3 ×q^2

P(3 heads) = 5 C 3 ×

(

1

2

) 3

×

(

1

2

) 2

P(3 heads) = 10 ×

1

8

×

1

4

P(3 heads) =

10

32

=

5

16

Therefore, the probability of seeing exactly 3 heads in 5 tosses is 165 , or 31.25%.

Practice

1. Look at the following graphs and indicate whether they could be binomial distributions. Explain how you
   know.

a.

b.

c.

d.

2. In question 1, suppose that the graphs that could be binomial distributions actually are binomial distributions.
   Which of these binomial distributions most closely approximates a normal distribution?