Answer:
The approximate probability is  [tex]P(X > 0.52) = P(Z > 0.2 ) = 0.42074[/tex]
Step-by-step explanation:
From the question we are told that
 The population proportion of Americans  that say the average person is not considerate of others when talking on a cellphone  is  p =  0.51
  The sample size is  n  =  100
Generally because the sample size is sufficiently  large the mean of this sampling distribution is
    [tex]\mu_{x} = p = 0.51[/tex]
Generally the standard deviation is mathematically represented as
  [tex]\sigma = \sqrt{ \frac{p(1 - p)}{n} }[/tex]
=> [tex]\sigma = \sqrt{ \frac{ 0.51 (1 - 0.51)}{100} }[/tex]
=> [tex]\sigma = 0.04999[/tex]
Generally  the sample proportion is mathematically represented as
    [tex]\^ p = \frac{52}{100}[/tex]
=> Â Â [tex]\^ p = 0.52[/tex]
Generally the probability that  52 or more Americans would indicate that the average person is not very considerate of others when talking on a cellphone is mathematically represented as
   [tex]P(X > 0.52) = P( \frac{X - \mu_{x}}{\sigma} > \frac{ 0.52 - 0.51}{0.04999} )[/tex]
[tex]\frac{X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ X )[/tex]
=> Â [tex]P(X > 0.52) = P(Z > 0.2 )[/tex]
From the z table  the area under the normal curve corresponding to  0.2 to the right is Â
   [tex]P(X > 0.52) = P(Z > 0.2 ) = 0.42074[/tex]
