Answer:
The probability is [tex]P( p > 0.585) = 0.044565 [/tex]
Step-by-step explanation:
From the question we are told that
The population proportion is p = 0.50
The sample size is n = 100
Gnerally the mean of the sampling distribution is
[tex]\mu_x = 0.50[/tex]
Generally the standard deviation of the sampling distribution is
[tex]\sigma = \sqrt{\frac{p(1- p)}{n} }[/tex]
=> [tex]\sigma = \sqrt{\frac{0.5 (1- 0.5)}{100} }[/tex]
=> [tex]\sigma =0.05[/tex]
Generally the approximate probability that the cable company will keep the shopping channel
[tex]P( p > 0.585) = P(\frac{p- \mu_{x}}{\sigma } > \frac{0.585 - 0.50}{0.05} )[/tex]
Generally [tex]\frac{p- \mu_{x}}{\sigma } = Z (The \ standardized \ value \ of p )[/tex]
=> [tex]P( p > 0.585) = P(Z > 1.7 )[/tex]
From the z-table the probability of (Z > 1.7 ) is
[tex]P(Z > 1.7 ) = 0.044565[/tex]
So [tex]P( p > 0.585) = 0.044565 [/tex]
