Question

A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of he experiment. 

n=9, p=0.3, x≤3

The probabity of x≤3 succenses is _______ (Round to four decimal places as needed.)

Answer 1

p = 0.3

1 - p = 1 - 0.3 = 0.7  

n = 9

(  x   3 )

Using binomial probability formula ,

p (  x   3 )  =p (x = 0 )+ p (x = 1) + p (x = 2)

= (9 ! (0 - 4)!) * 0.3³ * 0.7)⁴ +

  = (9 ! / (1 - 3)!) * 0.3⁴ * 0.7)³ +

  = (9 ! / (2 - 2)!) * 0.3⁵ * 0.7)²  +

  = (9 ! / ( 8 - 1)!) * 0.3⁶ * 0.7)¹ +

   = (9! / (9 - 0)!) * 0.3⁷ * 0.7)⁰  +

(  x   3 ) )  =0.7297

Probability = 0.7297