Answer to Question #312596 in Statistics and Probability for maggie

Question

Assume Binomial Distribution with n = 10 and p = 0.6. Please show your answers to 4 decimal places.

P(X = 4) =  

P(X ≤ 4) =   

P(X < 4) = 

P(X >4) =   

P(X ≥ 4) = 

Answer 1

$n=10 ~~p=0.6~~q=1-p=0.4$

(a) $P(X=4)$

$=\binom{n}{x}\times p^xq^{n-x}$

$=\binom{10}{4}\times0.6^40.4^6$

$=0.1115$

(b) $P(X\le4)$

$=P(4)+P(3)+P(2)+P(1)+P(0)$

$=0.1115+0.0425+0.0106+0.0016+0.0001$

$=0.1663$

(c) $P(X<4)$

$=P(3)+P(2)+P(1)+P(0)$

$=0.0425+0.0106+0.0016+0.0001$

$=0.0548$

(c) $P(X>4)$

$=1-P(X\le4)$

$=1-0.1663$

$=0.8337$