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]
=> [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]
=> [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
[tex]P(X > 0.52) = P(Z > 0.2 ) = 0.42074[/tex]
