8.3.1 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 ( X 3 ) = 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 = n p q = 10 × 1 4 × 3 4 = 1.875

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

Leave a Comment