X is a binomial random variable with parameters n 5 p 05 U

X is a binomial random variable with parameters n = 5, p = 0.5. Use the tables in Chapter 11 \"Chapter Tables\" to compute the probability indicated.

P(X 3)

P(X 3)

P(3)

P(0)

P(5)

X is a binomial random variable with the parameters shown. Use the tables in Chapter 11 \"Chapter Tables\" to compute the probability indicated.

n = 10, p = 0.25, P(X 6)

n = 10, p = 0.75, P(X 6)

n = 15, p = 0.75, P(X 6)

n = 15, p = 0.75, P(12)

n = 15, p=0.6, P(10X12)

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

a)
P( X < = 3) = P(X=3) + P(X=2) + P(X=1) + P(X=0)
= ( 5 3 ) * 0.5^3 * ( 1- 0.5 ) ^2 + ( 5 2 ) * 0.5^2 * ( 1- 0.5 ) ^3 + ( 5 1 ) * 0.5^1 * ( 1- 0.5 ) ^4 + ( 5 0 ) * 0.5^0 * ( 1- 0.5 ) ^5   
= 0.8125

b)
P( X < 3) = P(X=2) + P(X=1) + P(X=0)
= ( 5 2 ) * 0.5^2 * ( 1- 0.5 ) ^3 + ( 5 1 ) * 0.5^1 * ( 1- 0.5 ) ^4 + ( 5 0 ) * 0.5^0 * ( 1- 0.5 ) ^5
= 0.5
P( X > = 3 ) = 1 - P( X < 3) = 0.5

c)
P( X = 3 ) = ( 5 3 ) * ( 0.5^3) * ( 1 - 0.5 )^2
= 0.3125
d)
P( X = 0 ) = ( 5 0 ) * ( 0.5^0) * ( 1 - 0.5 )^5
= 0.0313
e)
P( X = 5 ) = ( 5 5 ) * ( 0.5^5) * ( 1 - 0.5 )^0
= 0.0313