Question

A paper reports that approximately 22% of cell phone owners walked into someone or something while they were talking on their cell phone. In a random sample of n = 200 cell phone owners, what is the probability that the sample proportion of cell phone owners who have walked into someone or something while they were on the phone would be less than 0.16? (Round your answer to four decimal places.)

Answer 1

Solution

Given that,

p = 0.22

1 - p = 1-0.22=0.78

n = 200

= p =0.22

=  [p ( 1 - p ) / n] =   [(0.22*0.78) / 200 ] = 0.02929

P( <0.16 ) =

= P[( - ) / < (0.16-0.22) / 0.02929]

= P(z <-2.05 )

Using z table,   

probability =0.0202