Answer:
0.3581<x<0.4429
Step-by-step explanation:
Using the formula for calculating the confidence interval of the population proportion p expressed as:
Confidence interval = p ± Z * √p(1-p)/n
p is the population proportion = x/n
p = 200/500
p = 0.4
Z is the z-score at 95% CI = 1.96
n is the sample size = 500
Substituting the given parameters into the formula we will have;
Confidence interval = 0.4 ± 1.96 * √p(1-p)/n
Confidence interval = 0.4 ± 1.96 * √0.4(0.6)/500
Confidence interval = 0.4 ± 1.96 * √0.24/500
Confidence interval = 0.4 ± 1.96 * √0.00048
Confidence interval = 0.4 ± 1.96 * 0.0219
Confidence interval = 0.4±0.04294
Confidence interval = (0.3571, 0.4429)
Hence the confidence interval of the population mean is 0.3581<x<0.4429
