Question

Consider the following binomial experiment. The probability that a green jelly bean is chosen at random from a large package of jelly beans is 1/8. If Sally chooses 13 jelly beans, what is the probability that at most two will be green jelly beans?

a) 0.7781

b) 0.5000

c) 0.2800

d) 0.7841

e) 0.2159

f) None of the above.

Consider the following binomial experiment: A company owns 5 copiers. The probability that on a given day any one copier will break down is 0.64. What is the probability that at least 3 copiers will break down on a given day?

a) 0.4398

b) 0.5075

c) 0.6417

d) 0.7491

e) 0.0024

f) None of the above.

Consider the following binomial experiment: A company owns 19 copiers. The probability that on a given day any one copier will break down is 11/100. Find the mean number of copiers that will break down on any given day.

a) 0.21

b) 2.09

c) 1.73

d) 1.10

e) 1.90

f) None of the above.

Answer 1

1)solution:

Given that,
n= 13, p= 1/8=0.125
q=0.875
Let X be a random variable which denotes the number of green jelly bean .
X~ binomial distribution (n=13,p=0.125)
The pmf of the binomial random variable X is given by
P(X=x)= (nCx) (p^x) [q^(n-x)] , where q=1-p
=(13Cx)(0.125^x) [0.875^(13-x)]
P(X<=2)= P(X=0)+P(X=1)+P(X=2)
=(13C0)(0.125^0) [0.875^(13-0)]
+(13C1)(0.125^1) [0.875^(13-1)]
+(13C2)(0.125^2) [0.875^(13-2)]
=0.1762+0.3273+0.2805
=0.7840
The probability that at most two will be green jelly beans is 0.7840
Answer:
d) 0.7841
2)

Given that

n=5, p= 0.64

q=0.36
Let X be a random variable which denotes the number of copiers will break down on a given day.
X~ binomial distribution (n=5,p=0.64)
The pmf of the binomial random variable X is given by
P(X=x)= (nCx) (p^x) [q^(n-x)] , where q=1-p
=(5Cx)(0.64^x) [0.36^(5-x)]
P(X>=3)=P(X=3)+ P(X=4)+P(X=5)
=(5C3)(0.64^3) [0.36^(5-3)]
+(5C4)(0.64^4) [0.36^(5-4)]
+(5C5)(0.64^5) [0.36^(5-5)]
=0.3397+0.3020+0.1074
=0.7491
the probability that at least 3 copiers will break down on a given day is 0.7491
Answer :
d) 0.7491
3)
Given that,
n= 19,p= 11/100=0.11
q=0.89
Let X be a random variable which denotes the number of copiers will break down on a given day.
X~ binomial distribution (n=19,p=0.11)
The mean of the binomial distribution is given as
Mean=n×p
=19×0.11
=2.09
Answer:
b) 2.09