Respuesta :
Answer:
D. 68%
Step-by-step explanation:
The following statistics are given;
sample mean = 47%
s = 5% ; the sample standard deviation
n = 625 ; the sample size
The confidence interval for a population mean is given as;
sample mean ± z-score*[tex]\frac{s}{\sqrt{n} }[/tex]
Substituting the above values we have;
47 ± z-score*[tex]\frac{5}{\sqrt{625} }[/tex]
47 ± z-score*0.2
The confidence interval has been given as;
lower limit = 46.8%
upper limit = 47.2%
We can use any of these two values with the above expression to solve for the z-score. Using the lower limit we have the following equation;
47 - z-score*0.2 = 46.8
-z-score*0.2 = 46.8 - 47
-z-score*0.2 = -0.2
z-score = 1
The area of the standard normal curve between -1 and +1 will be the confidence level for the given confidence interval.
Pr( -1<Z<1 ) = 0.68 = 68%
From the Empirical rule
