Question

A recent survey found that 30% of telephone users have switched completely to cell phone use (i.e. they do not have landlines in their homes). A random sample of 10 of these customers is selected. Would it be considered unusual if there was 1 telephone user in this sample without a landline

Answer 1

it cannot be considered unusual if there was 1 telephone user in this sample without a landline

Explanation:

Given that a recent survey found that 30% of telephone users have switched completely to cell phone use (i.e. they do not have landlines in their homes)

Each telephone user is independent of the other and hence prob for switching to cell phone has constant probability 0.30

X the no of customers who switch to cell phones from the sample of 10 is

Binomial with n =10 and p = 0.30

Prob (x=1) = Prob there was 1 telephone user in this sample without a landline

=
`10C1 (0.3)^1 (0.7)^9\\= 0.1211`

This is not very near to 0.

Hence this is not a rare event.

So it cannot be considered unusual if there was 1 telephone user in this sample without a landline