Probability Distribution, Short Questions (Question 1 & 2)


Question 1:
Diagram below shows the graph of a binomial distribution of X.
(a) the value of h,
(b) P (X ≥ 3)

Solution:
(a)
P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4) = 1
1 16 + 1 4 +h+ 1 4 + 1 16 =1 h=1 5 8 h= 3 8  

(b)
P (X ≥ 3) = P (X = 3) + P (X = 4)
P( X3 )= 1 4 + 1 16 = 5 16


Question 2:
The random variable X represents a binomial distribution with 10 trails and the probability of success is ¼.
(a) the standard deviation of the distribution,
(b) the probability that at least one trial is success.

Solution:
(a)
n = 10, p = ¼
Standard deviation= npq                               = 10× 1 4 × 3 4                               =1.875

(b)
P(X=r)= C 10 r ( 1 4 ) r ( 3 4 ) 10r P(X1) =1P(X<1) =1P( X=0 ) =1 C 10 0 ( 1 4 ) 0 ( 3 4 ) 10 =0.9437