p35 of the applications received for a particular credit car

p=35% of the applications received for a particular credit card are accepted. A simple random sample of next n=6 applications is selected. X Number of applications accepted. Based on binomial distribution function, find the probability that none of the applications will be accepted, that is, find P(X= 0). Based on binomial distribution tabic, find the probability that at least one application will be accepted, that is. find P(x>1)

Solution

a) here,prob. of success= p = 0.35..n=6..

P [ X = 0 ] = ( 6 C 0 ) ( 0.35) ^ 0 * ( 1 - 0.35 ) ^ 6 = 0.075419......

B) P [ X >= 1 ] = 1 - P [ X < 1 ] = 1 - P [ X = 0 ] = 1 - 0.075419 = 0.924581.....

C) E ( X ) = n*p = 6 * 0.35 = 2.1 and VAR( X) = n*p*( 1 - p) = 1.365........