Question

A large city in a Western State has believes that 60% of its citizens support the addition of an ombudsmen among its city council members. Assuming they are correct, find the probability that if they polled 2400 people, the percent who have similar beliefs about this role would be less than 61.5%. (Answer should be to 4 decimals.)

Answer 1

Solution:
Given in the question
Population proportion of A large city in a Western State has believes of its citizens support the addition of an ombudsmen among its city council members = 0.60
Number of sample(n) = 2400
We need to calculate percent who have similar beliefs about this role would be less than 61.5% i.e. P(p^<0.615) = ?
Here we will use standard normal distribution, First we will calculate Z-score, which can be calculated as
Z-score = (p^ - p)/sqrt(p*(1-p)/n) = (0.615-0.60)/sqrt(0.6*(1-0.6)/2400) = 1.5
From Z table we found p-value
P(p^<0.615) = 0.9332
So there is 93.32% who have similar beliefs about this role would be less than 61.5%.