Abuilding manager installs sensors to see how often people turn off the lights when they leave the room. after a month the manager has a sample size of 625, a sample mean of 47%, and a sample standard deviation of 5%. what is the confidence level for a confidence interval of 46.8% to 47.2%? a. 85% b. 99.7% c. 95% d. 68%

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*

Substituting the above values we have;

47 ± z-score*

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

expression #3 is not equivalent. the others are.