\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
An orchard manager selects a random sample of 64 apples to estimate the harvest quality. The sample mean weight is \(150\) g with a sample standard deviation of \(s_n = 12\) g.
  1. Justify the use of the \(z\)-interval for this estimation.
  2. Calculate the \(99\pourcent\) confidence interval for the mean weight of an apple.

Capture an image of your work. AI teacher feedback takes approximately 10 seconds.