Abuilding 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.

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step-by-step explanation:

probably .5

i can on others if necessary.