5. A factory produces steel sheets whose weights, \(X \mathrm {~kg}\), have a normal distribution with an unknown mean \(\mu \mathrm { kg }\) and known standard deviation \(\sigma \mathrm { kg }\). A random sample of 25 sheets gave both a

• \(95 \%\) confidence interval for \(\mu\) of \(( 30.612,31.788 )\)
• \(c \%\) confidence interval for \(\mu\) of \(( 30.66,31.74 )\)
  1. Find the value of \(\sigma\)
  2. Find the value of \(c\), giving your answer correct to 3 significant figures.