Question

A recent study conducted by a health statistics center found that 27​% of households in a certain country had no landline service. This raises concerns about the accuracy of certain​ surveys, as they depend on​ random-digit dialing to households via landlines. Pick five households from this country at random.

a) What is the probability that all five of them have a​ landline?

b) What is the probability that at least one of them does not have a​ landline?

c) What is the probability that at least one of them does have a​ landline?

A national survey found that 45​% of adults ages​ 25-29 had only a cell phone and no landline. Suppose that three 25-29-year-olds are randomly selected.

a) What is the probability that all of these adults have only a cell phone and no​ landline?

b) What is the probability that none of these adults have only a cell phone and no​ landline?

c) What is the probability that at least one of these adults has only a cell phone and no​ landline?

Answer 1

1.

P( certain household had no landline service) = 0.27 =p

A 5 households from this country is selected. n= 5

Let X be the number of households that has no landline

X~ Binomial ( 5, 0.27)

a) Probability that all five of them have a​ landline = P( None of them have no landline)

= P( X=0)

= ( 1-0.27)^ 5

= 0.2073

  b) P( At least one of them does not have a landline) = P( X >=1)

= 1 - P( X < 1)

= 1- P( X=0)

= 1- 0.2073

= 0.7927

  c) P( At least one of them does have a landline) = P( At most 4 of then doesnot have a landline)

= P( X <=4)

=0.9986

2) P( adults ages​ 25-29 had only a cell phone and no landline ) = 0.45 = p

A random sample of 3 adult is selected, n= 3

Let X be the number of adults that have only a cell phone and no landline.

a) P(X= 3) = (0.45) ^ 3 = 0.091125

b) P( X=0) = ( 1-0.45) ^3 = 0.166375

c) P( X >= 1) = 1- P( X <1)

= 1- P( X=0)

= 1- 0.166375

= 0.833625