Binomial Distribution
Question
Q1.
It is known as that 10% of the items produced in a factory are defective . If a sample of 400 items is selected at random then find
the mean and variance of defective items .
(a) 33
(b) 36
(c) 30
(d) 31
Solution. b
In this case n = 400 , p = 0.10 and q = 0.90
∴ p + q = 1
mean = np = 400 x 0.1 = 40
variance = npq = 400 x 0.1 x 0.9 = 36
Solution
Q2.
Binomial distribution is unimodal or bimodal if n = 10 and p = 0.5 .
(a) Bimodal
(b) Unimodal
(c) none
(d) can't say
Solution. b
Formula of mode is = (n + 1)p
Mode = (10 + 1) (0.5) = (11)(0.5) = 5.5
5.5 is non-integer , so mode is higher
integral part that is 5 .
So, Binomial distribution is Unimodal .
Solution
Q3.
If P <
1/2
, Binomial distribution
is .
(a) symmetrical
(b) negatively skewed
(c) positively skewed
(d) can't say
Solution. c
positively skewed
Solution
Q4.
Find maximum variance if n = 9 and q = 0.5 .
(a) 1.75
(b) 4
(c) 2
(d) 2.25
Solution. d
Maximum variance =
n/4
=
9/4
= 2.25
Solution
Q5.
n is very large , p and q are not small then binomial distribution tends to .
(a) Normal distribution
(b) poisson distribution
(c) chi-square distribution
(d) none
Solution. a
Normal distribution
Solution
