A binomial random unable has meen equal to 200 and a standar

A binomial random unable has meen equal to 200 and a standard deviation of 10. Find the value of n and p.

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

Mean ( np ) = 200 -----------------(1)
Standard Deviation ( npq )= 10 -----------(2)

Substitute (1) in (2)
( npq )= 10
=> ( 200q )= 10
=> 200q = 100
=> q = 100/200 = 0.5

p = 1 - q = 1 - 0.5 = 0.5
From (1) np = 200 = > n(0.5) = 200 => n = 200/0.5 = 400

[ANSWERS] n = 400, p = 0.50