1. A manufacturing company produces steel housings for electrical equipment. The main component of the housing is a steel trough made out of a 2-mm steel coil. The width of the troughs is critical because of weatherproofing in outdoor situations.The mean width of a sample of 49 troughs is calculated to be 204.21. Assuming that the population standard deviation is 0.46mm, calculate a 95% confidence interval for the mean width of the troughs and interpret.Show your answers to three decimal places.

2. Note: This question is different to question 1

A manufacturing company produces steel housings for electrical equipment. Themain component of the housing is a steel trough made out of a 2-mm steel coil. Thewidth of the troughs is critical because of weatherproofing in outdoor situations.A sample of 49 troughs were checked and the following sample statistics calculated204.209 x = , 0.461 s= .(a) Find the appropriate critical values and calculate a 95% confidence interval for the mean width of the troughs and interpret.Show your answers to three decimal places.(b) What degrees of freedom did you use when consulting the table? How inaccurate do you think your answer might be compare to the use of Excel?