A researcher is studying the approval rating of a political candidate in a city. The population consists of 10,000 registered voters. a. Given that the true proportion of voters who approve of the candidate is 0.60, calculate the probability that a random sample of 200 voters will have a sample proportion of approval less than 0.55. b. Given that the true proportion of voters who approve of the candidate is 0.60, calculate the probability that a random sample of 200 voters will have a sample proportion of approval greater than 0.63. c. Given that the true proportion of voters who approve of the candidate is 0.60, calculate the probability that a random sample of 200 voters will have a sample proportion of approval within 2% of the true proportion.
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likesAnswer to a math question A researcher is studying the approval rating of a political candidate in a city. The population consists of 10,000 registered voters. a. Given that the true proportion of voters who approve of the candidate is 0.60, calculate the probability that a random sample of 200 voters will have a sample proportion of approval less than 0.55. b. Given that the true proportion of voters who approve of the candidate is 0.60, calculate the probability that a random sample of 200 voters will have a sample proportion of approval greater than 0.63. c. Given that the true proportion of voters who approve of the candidate is 0.60, calculate the probability that a random sample of 200 voters will have a sample proportion of approval within 2% of the true proportion.
4.61. Calculate z-score for \( \hat{p} < 0.55 \):
2. Find \( P(\hat{p} < 0.55) \) using standard normal tables:
b.
1. Calculate z-score for \( \hat{p} > 0.63 \):
2. Find \( P(\hat{p} > 0.63) \) using \( P(z > 0.8651)\):
c.
1. Calculate z-score for \( \hat{p} = 0.58 \):
2. Calculate z-score for \( \hat{p} = 0.62 \):
3. Find probability \( P(0.58 < \hat{p} < 0.62) \):