The following sample observations were randomly selected. $($Do not round the intermediate values. Negative amount should be indicated by a minus sign. Round your answers to $3$ decimal places.$)$

x: $553610$

y: $46567$

a$.$ Determine the $98\%$ confidence interval for the mean predicted when x $=6.$

b$.$ Determine the $98\%$ prediction interval for an individual predicted when x $=6.$