Question

A steel mill’s milling machine produces steel rods that are supposed to be 5 cm in diameter. When the machine is in statistical control, the rod diameters vary according to a Normal distribution with mean µ = 5 cm. A large sample of 150 rods produced by the machine yields a mean diameter of 5.005 cm and a standard deviation of 0.02 cm.

Construct a 99% confidence interval for the true mean diameter of the rods produced by the milling machine. Follow the inference toolbox.

Answer 1

99% confidence interval for the true mean diameter of the rods produced by the milling machine is between a lower limit of 5.0007 cm and an upper limit of 5.0093 cm.

Explanation:

Confidence interval = mean + or - Error margin (E)

mean = 5.005 cm

sd = 0.02 cm

n = 150

degree of freedom = n - 1 = 150 - 1 = 149

confidence level = 99%

t-value corresponding to 149 degrees of freedom and 99% confidence level is 2.6093

E = t×sd/√n = 2.6093 × 0.02/√150 = 0.0043 cm

Lower limit = mean - E = 5.005 - 0.0043 = 5.0007 cm

Upper limit = mean + E = 5.005 + 0.0043 = 5.0093

99% confidence level for the true mean diameter is between 5.0007 cm and 5.0093 cm