Assume that a sample is used to estimate a population proportion μ\displaystyle \mu. Find the margin of error M.E. that corresponds to a sample of size 19 with a mean of 52.4 and a standard deviation of 10.1 at a confidence level of 99.9%.

Report ME accurate to one decimal place because the sample statistics are presented with this accuracy.
M.E. =

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.