If, for a random sample of 16 days, the sample mean ends up being exactly one standard deviation of x above the population mean, what is the sample mean for those 16 days?

The answer to the question is

μx + (σx/4)

Step-by-step explanation:

The sample mean that is one standard deviations above the population mean  is given by

value = μx + (Number of standard deviations)

(σx/√n)

value = μx + 1 (σx/√16)=

=  μx + (σx/4) =

Where

μx = Population mean

σx = Population standard deviation

n = Sample size

The standard error of the mean is

σ/√n =σ/√16 = σ/4

The standard of error is an indication of the expected error in the mean of a sample from the mean of the population.

The above statements is based on the central limit theorem, which states that, in particular instances the normalized sum of independent random variables becomes closer and closer to those of  normal distribution regardless of the variation in the sample of the variables