A building manager installs sensors to see how often people turn off the lights when they leave a room. After a month, the manager has a sample size of 400, a sample mean of 47%, and a sample standard deviation of 4%. What is the confidence level for a confidence interval of 46.6% to 47.4%?

A. 68%

B. 85%

C. 99.7%

D. 95%

The answer is C.

The figures in your problem are inconsistent with the data.

The sample std deviation is not and cannot be. 04 (4%).

the sample std dev is sqrt[ (.47) (1-.47) / 400]=.02495.

The margin of error from your CI is. 474 -.47 =.004 (very small).

This would represent. 02495/.004 = 6.24 std dev. from expected, which would have a very

high level of confidence (99.97 ... %). Something is likely wrong with the figures in your problem.