Suppose that, based on a sample, the 99.7% confidence interval for the mean of a population is (14, 44). what is the value of s/√n

Population mean = (14,44)
Z at 99.7% = 2.96

Therefore,
Sample mean = (14+44)/2 = 29

However,
Population mean = Sample mean +/- Z*s/Sqrt (n)

Taking one of the ranges, say lower range:
14 = 29-Z*s/Sqrt (n)
14-29 = - 2.96*s/Sqrt (n)
-15 = -2.96*s/Sqrt (n)
5 = s/Sqrt (n)

Therefore,