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A radio station believes that the proportion of people who listen to the radio on their way to work is 0.81. They take a random sample of 304 people. Use the Central Limit Theorem for Proportions to find the probability that more than 266 of them listen to the radio on their way to work. Round z-scores to 2 decimals. Round your final answer to 4 decimals.

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Answer:

z=2.89

p=0.0019

Step-by-step explanation:

z-scores can be found using the formula

z=[tex]\frac{X-p}{\frac{\sqrt{p*(1-p)} }{\sqrt{N} } }[/tex] where

  • X is the sample proportion who listen to the radio on their way to work ([tex]\frac{266}{304} =0.875[/tex])
  • p is the believed proportion of people who listen to the radio on their way to work  (0.81)
  • N is the sample size

then

z=[tex]\frac{0.875-0.81}{\frac{\sqrt{0.81*(0.19)} }{\sqrt{304} } }[/tex] ≈2.89 and

p=0.0019

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