finding the minimum sample size in estimation

Problem:
A production engineer wishes to estimate, with a 95% confidence interval, the yearly income of welders with at least five years experience to within $1,000. He estimates that the range of incomes is no more than $24,000, so using the Empirical Rule he estimates the population standard deviation to be about one-sixth as much, or about $4,000. Find the estimated minimum sample size required. 

Solution:

#inputs:
Error = 1000
std_d = 4000
alfa = 0.95 #desired confidence interval 

#finding the z-value:
z_vale = qnorm((1- alfa)/2, 
               mean = 0, 
               sd = 1)

#finding the minimum sample size:
sample_size = ceiling(((z_vale^2)*(std_d^2))/(Error^2))
sample_size

conclusion: 
the production engineer needs at least 62 samples to estimate the salary of the welders with a 95% confidence interv
al and $1000 error.

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