1 If n 5 and pi 040 a PX 4 00768 b PX 3 09130 c PX 2

1) If n = 5 and (pi) = 0.40,

a) P(X) = 4 = 0.0768

b) P(X) 3 = 0.9130

c) P(X) < 2 = 0.3370

With 15 observations,

a) the smallest of the standard normal quartile values covers an area under the normal curve of ___ /16 = ____ . The corresponding Z-value is -1.53.

b) The largest of the standard normal quantile values covers an area under the normal curve of ___ /16 = ____ . The corresponding Z-value is +1.53.

c) The middle of the standard quantile values covers an area under the normal curve of ___ /16 = _____ . The corresponding Z-value is 0.00.

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

P( X = 4 ) = ( 5 4 ) * ( 0.4^4) * ( 1 - 0.4 )^1
= 0.0768

P( X < = 3) = P(X=3) + P(X=2) + P(X=1) + P(X=0)   
= ( 5 3 ) * 0.4^3 * ( 1- 0.4 ) ^2 + ( 5 2 ) * 0.4^2 * ( 1- 0.4 ) ^3 + ( 5 1 ) * 0.4^1 * ( 1- 0.4 ) ^4 + ( 5 0 ) * 0.4^0 * ( 1- 0.4 ) ^5   
= 0.913

P( X < 2) = P(X=1) + P(X=0)
= ( 5 1 ) * 0.4^1 * ( 1- 0.4 ) ^4 + ( 5 0 ) * 0.4^0 * ( 1- 0.4 ) ^5 +   
= 0.337

Note: Post the remaining parts in diffrent threadd