Question

Let X be a binomial random variable with parameters (n, p). Find the approximate value of P(|X| > a) when n is sufficiently large using the central limit theorem, where a is a positive number. g

Answer 1

Answer:

Approximate value of P(|X| > a)  is attached below

Ф ( 0 ) is the CDF of standard Normal variate

Step-by-step explanation:

x ~ Bin ( n, p )

E ( x ) = np ,  Var ( x ) = np ( 1 - p )

∴ Z = Iin    ( x - E(x) ) / √Var x )   ~ N ( 0, 1 )  ( this is the standard normal Variate)

        n-1∞

Find the approximate value of P(|X| > a)

Ф ( 0 ) is the  CDF of standard Normal variate

attached below is the remaining part of the solution