A quаlity cоntrоl mаnаger at a factоry wants to estimate the average length of bolts produced by a new machine. The standard deviation (( sigma )) of the bolt lengths is known to be 0.1 mm. She takes a random sample of 50 bolts (( n = 50 )) and finds the sample mean (( overline{x} )) is 50.5 mm. Using the formula below, where ( z = 1.96 ) is the z-score corresponding to the 95% confidence level, compute the 95% confidence interval for the true mean bolt length. Formula: (text{Confidence Interval} = bar{x} pm z left(frac{sigma}{sqrt{n}}right))