Sampling Mean Problem

Question

A water bottler sells spring water. The machines are set such that on average, 1.02 liters
are dispensed with a known standard deviation of 0.06 liters. The firm routinely collects a
random sample of bottles and tests whether the machine is dispensing correctly. Suppose
the machine is working properly. What is the chance that in a random sample of 36
bottles, the sample mean will be within 0.05 liters of the specified level?

Answer 1

 

 

  the margin of error is k * stddev/sqrt(n) where k is the confidence level constant from the normal table

 

   0.05  = k* 0.06/sqrt(36)

 

  0.05 = k * 0.06/6

 

  0.05 = k * 0.01

 

  5 = k

 

The reason why the probability is so high is because

the standard deviation = 0.06 > 0.05 = margin of error