Question

About 40% of adults use cash for payments. Suppose four adults were randomly selected.

a. What kind of probability is this? Explain why.

b. What is the probability that one of the adults use cash for payments?

c. What is the probability that more than three adults use cash for payments?

d. What is the mean and variance? Interpret your results.

Answer 1

Solution:-

Proportion of adults using cash p=0.4 and

sample size=4.

Here suppose adult using cash for payment is the success of our interest.

A)

The probability is binominal since we have p as probability of success & n as bernouli.

Here X:no of adults using cash for payment,

Hence X follows binominal distribution with

n=4 &p=0.4.

Hence pmf of X is

here x=0,1,2,3,4.

B)

Here we have to find P(X=1)

D)

Here X~Binominal (n,p).

hence mean of X=np

=4*0.4=1.6

i.e.,on an average 3 adults in sample use cash for payments.

& variance of X=np(1-p)

=1.6(1-0.4)=1.6*0.6

Variance=0.96

i.e.,on an average adults in sample use cash for payments.