Using the formula for z scores solve the equation for the me

Using the formula for z scores, solve the equation for the mean and also for n

Solution

Z-score = X -mean/std/sqrt(n)

where std = standard deviation and X is the value at which Z-score is calculated

X - mean = Z-score *std//sqrt(n)

Mean = X - ((Z-score*std)/sqrt(n))

for n

std/sqrt(n) = X- mean/Z-score

sqrt(n) = std * Z-score/X-mean

n = (std * Z-score/X-mean)^2