estimation on average manufacturing time for a specific product with sampling procedure



Production Engineering department has randomly selected a sample of 49 units of product one. From the sample, the whole processing time on this product has an average of 35 minutes with 14 minutes standard deviation. The production engineer is interested to estimate the confidence interval on the average manufacturing time of this product with 98% precision:


#input:
sample_mean = 35
sample_size = 49
std_d = 14 #if standard deviation of the population is available then use it;
            otherwise, we use sample standard deviation 
alfa = 0.98 #precision of the confidence interval 

#finding the z-value:
z_vale = qnorm((1- alfa)/2, 
              mean = 0, 
              sd = 1)
#constructing error:
Error = z_vale*(std_d/sqrt(sample_size))

#Constructing the interval:

c(sample_mean + Error, sample_mean - Error)

According to the results, the product engineer has estimated with 98% confidence that the manufacturing time on this product will be approximately between 31 to 40 minutes


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